How to Find the Least Common Denominator

PDF download Download Article
PDF download Download Article

In order to add or subtract fractions with different denominators (the bottom number of the fraction), you must first find a common denominator shared between them. In order to have the simplest fraction at the end, it is best to find not just a common denominator, but the least (or smallest) common denominator. This refers to the lowest multiple shared by each original denominator in the equation, or the smallest whole number that can be divided by each denominator. [1] You may also see the phrase least common multiple . This generally refers to whole numbers, but the methods to find it are the same for both. Determining the least common denominator allows you convert the denominators to the same number so you can then add and subtract them.

Method 1
Method 1 of 4:

Listing Multiples

PDF download Download Article
  1. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/c\/c6\/Find-the-Least-Common-Denominator-Step-1-Version-2.jpg\/v4-460px-Find-the-Least-Common-Denominator-Step-1-Version-2.jpg","bigUrl":"\/images\/thumb\/c\/c6\/Find-the-Least-Common-Denominator-Step-1-Version-2.jpg\/aid2948791-v4-728px-Find-the-Least-Common-Denominator-Step-1-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    Make a list of several multiples for each denominator in the equation. Each list should consist of the denominator numeral multiplied by 1, 2, 3, 4, and so on. [2]
    • Example: 1/2 + 1/3 + 1/5
    • Multiples of 2: 2 * 1 = 2; 2 * 2 = 4; 2 * 3 = 6; 2 * 4 = 8; 2 * 5 = 10; 2 * 6 = 12; 2 * 7 = 14; etc.
    • Multiples of 3: 3 * 1 = 3; 3 * 2 = 6; 3 *3 = 9; 3 * 4 = 12; 3 * 5 = 15; 3 * 6 = 18; 3 * 7 = 21; etc.
    • Multiples of 5: 5 * 1 = 5; 5 * 2 = 10; 5 * 3 = 15; 5 * 4 = 20; 5 * 5 = 25; 5 * 6 = 30; 5 * 7 = 35; etc.
  2. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/1\/18\/Find-the-Least-Common-Denominator-Step-2-Version-2.jpg\/v4-460px-Find-the-Least-Common-Denominator-Step-2-Version-2.jpg","bigUrl":"\/images\/thumb\/1\/18\/Find-the-Least-Common-Denominator-Step-2-Version-2.jpg\/aid2948791-v4-728px-Find-the-Least-Common-Denominator-Step-2-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    Scan through each list and mark any multiples that are shared by all of the original denominators. After identifying the common multiples, identify the lowest multiple common to all the denominators. [3]
    • Note that if no common multiple exists at this point, you may need to continue writing out multiples until you eventually come across a shared multiple.
    • This method is easier to use when small numbers are present in the denominator.
    • In this example, the denominators only share one multiple and it is 30: 2 * 15 = 30 ; 3 * 10 = 30 ; 5 * 6 = 30
    • The LCD = 30
    Advertisement
  3. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/a\/ad\/Find-the-Least-Common-Denominator-Step-3-Version-2.jpg\/v4-460px-Find-the-Least-Common-Denominator-Step-3-Version-2.jpg","bigUrl":"\/images\/thumb\/a\/ad\/Find-the-Least-Common-Denominator-Step-3-Version-2.jpg\/aid2948791-v4-728px-Find-the-Least-Common-Denominator-Step-3-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    In order to change each fraction in the equation so that it remains true to the original equation, you will need to multiply each numerator (the top of the fraction) and denominator by the same factor used to multiply the corresponding denominator when reaching the LCD. [4]
    • Example: (15/15) * (1/2); (10/10) * (1/3); (6/6) * (1/5)
    • New equation: 15/30 + 10/30 + 6/30
  4. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/d\/d4\/Find-the-Least-Common-Denominator-Step-4-Version-2.jpg\/v4-460px-Find-the-Least-Common-Denominator-Step-4-Version-2.jpg","bigUrl":"\/images\/thumb\/d\/d4\/Find-the-Least-Common-Denominator-Step-4-Version-2.jpg\/aid2948791-v4-728px-Find-the-Least-Common-Denominator-Step-4-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    After finding the LCD and changing the fractions accordingly, you should be able to solve the problem without further difficulty. Remember to simplify the fraction at the end. [5]
    • Example: 15/30 + 10/30 + 6/30 = 31/30 = 1 1/30
    5. Advertisement
Method 2
Method 2 of 4:

Using the Greatest Common Factor [6]

PDF download Download Article
  1. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/9\/93\/Find-the-Least-Common-Denominator-Step-5-Version-2.jpg\/v4-460px-Find-the-Least-Common-Denominator-Step-5-Version-2.jpg","bigUrl":"\/images\/thumb\/9\/93\/Find-the-Least-Common-Denominator-Step-5-Version-2.jpg\/aid2948791-v4-728px-Find-the-Least-Common-Denominator-Step-5-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    The factors of a number are all of the whole numbers that are evenly divisible into that number. [7] The number 6 has four factors: 6, 3, 2, and 1. (Every number has a factor of 1, because every number can be evenly divided by 1.)
    • For example: 3/8 + 5/12.
    • Factors of 8: 1, 2, 4, and 8
    • Factors of 12: 1, 2, 3, 4, 6, 12
  2. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/c\/cc\/Find-the-Least-Common-Denominator-Step-6-Version-2.jpg\/v4-460px-Find-the-Least-Common-Denominator-Step-6-Version-2.jpg","bigUrl":"\/images\/thumb\/c\/cc\/Find-the-Least-Common-Denominator-Step-6-Version-2.jpg\/aid2948791-v4-728px-Find-the-Least-Common-Denominator-Step-6-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    Once you have listed the factors of each denominator, circle all of the common factors. The largest of the common factors is the greatest common factor (GCF) that will be used to continue solving the problem.
    • In our example, 8 and 12 share the factors 1, 2, and 4.
    • The greatest common factor is 4.
  3. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/d\/db\/Find-the-Least-Common-Denominator-Step-7-Version-2.jpg\/v4-460px-Find-the-Least-Common-Denominator-Step-7-Version-2.jpg","bigUrl":"\/images\/thumb\/d\/db\/Find-the-Least-Common-Denominator-Step-7-Version-2.jpg\/aid2948791-v4-728px-Find-the-Least-Common-Denominator-Step-7-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    In order to use the greatest common factor to solve the problem, you must first multiply the two denominators together.
    • Continuing our example: 8 * 12 = 96
  4. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/b\/ba\/Find-the-Least-Common-Denominator-Step-8-Version-2.jpg\/v4-460px-Find-the-Least-Common-Denominator-Step-8-Version-2.jpg","bigUrl":"\/images\/thumb\/b\/ba\/Find-the-Least-Common-Denominator-Step-8-Version-2.jpg\/aid2948791-v4-728px-Find-the-Least-Common-Denominator-Step-8-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    After finding the product of the two denominators, divide that product by the GCF you found previously. This number will be your least common denominator (LCD). [8]
    • Example: 96 / 4 = 24
  5. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/b\/b4\/Find-the-Least-Common-Denominator-Step-9-Version-2.jpg\/v4-460px-Find-the-Least-Common-Denominator-Step-9-Version-2.jpg","bigUrl":"\/images\/thumb\/b\/b4\/Find-the-Least-Common-Denominator-Step-9-Version-2.jpg\/aid2948791-v4-728px-Find-the-Least-Common-Denominator-Step-9-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    To determine the multiple needed to make the denominators equal, divide the LCD you determined by the original denominator. Multiply the numerator and the denominator of each fraction by this number. The denominators should now both be equal to the LCD. [9]
    • Example: 24 / 8 = 3; 24 / 12 = 2
    • (3/3) * (3/8) = 9/24; (2/2) * (5/12) = 10/24
    • 9/24 + 10/24
  6. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/6\/63\/Find-the-Least-Common-Denominator-Step-10-Version-2.jpg\/v4-460px-Find-the-Least-Common-Denominator-Step-10-Version-2.jpg","bigUrl":"\/images\/thumb\/6\/63\/Find-the-Least-Common-Denominator-Step-10-Version-2.jpg\/aid2948791-v4-728px-Find-the-Least-Common-Denominator-Step-10-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    With the LCD found, you should be able to add and subtract the fractions in the equation without further difficulty. Remember to simplify the fraction at the end, if possible.
    • Example: 9/24 + 10/24 = 19/24
    7. Advertisement
Method 3
Method 3 of 4:

Factoring Each Denominator into Primes

PDF download Download Article
  1. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/b\/b0\/Find-the-Least-Common-Denominator-Step-11-Version-2.jpg\/v4-460px-Find-the-Least-Common-Denominator-Step-11-Version-2.jpg","bigUrl":"\/images\/thumb\/b\/b0\/Find-the-Least-Common-Denominator-Step-11-Version-2.jpg\/aid2948791-v4-728px-Find-the-Least-Common-Denominator-Step-11-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    Factor each denominator digit into a series of prime numbers that multiply together to make that number. Prime numbers are numbers that cannot be divided by any other number. [10]
    • Example: 1/4 + 1/5 + 1/12
    • Prime factorization of 4: 2 * 2
    • Prime factorization of 5: 5
    • Prime factorization of 12: 2 * 2 * 3
  2. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/2\/27\/Find-the-Least-Common-Denominator-Step-12-Version-2.jpg\/v4-460px-Find-the-Least-Common-Denominator-Step-12-Version-2.jpg","bigUrl":"\/images\/thumb\/2\/27\/Find-the-Least-Common-Denominator-Step-12-Version-2.jpg\/aid2948791-v4-728px-Find-the-Least-Common-Denominator-Step-12-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    Tally up the number of times that each prime number appears in the factorization of each denominator digit. [11]
    • Example: There are two 2’s in 4; zero 2’s in 5; two 2’s in 12
    • There are zero 3’s in 4 and 5; one 3 in 12
    • There are zero 5’s in 4 and 12; one 5 in 5
  3. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/2\/20\/Find-the-Least-Common-Denominator-Step-13-Version-2.jpg\/v4-460px-Find-the-Least-Common-Denominator-Step-13-Version-2.jpg","bigUrl":"\/images\/thumb\/2\/20\/Find-the-Least-Common-Denominator-Step-13-Version-2.jpg\/aid2948791-v4-728px-Find-the-Least-Common-Denominator-Step-13-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    Identify the largest number of times you used each prime number for any of the denominators and note that count.
    • Example: The largest count of 2 is two; the largest of 3 is one; the largest of 5 is one
  4. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/0\/0c\/Find-the-Least-Common-Denominator-Step-14-Version-2.jpg\/v4-460px-Find-the-Least-Common-Denominator-Step-14-Version-2.jpg","bigUrl":"\/images\/thumb\/0\/0c\/Find-the-Least-Common-Denominator-Step-14-Version-2.jpg\/aid2948791-v4-728px-Find-the-Least-Common-Denominator-Step-14-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    Do not write out the number of times each prime number appeared throughout all the original denominators. Only write out the largest count, as determined in the previous step.
    • Example: 2, 2, 3, 5
  5. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/5\/59\/Find-the-Least-Common-Denominator-Step-15-Version-2.jpg\/v4-460px-Find-the-Least-Common-Denominator-Step-15-Version-2.jpg","bigUrl":"\/images\/thumb\/5\/59\/Find-the-Least-Common-Denominator-Step-15-Version-2.jpg\/aid2948791-v4-728px-Find-the-Least-Common-Denominator-Step-15-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    Multiply the prime numbers together as they appeared in the previous step. The product of these numbers equals the LCD for the original equation. [12]
    • Example: 2 * 2 * 3 * 5 = 60
    • LCD = 60
  6. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/9\/90\/Find-the-Least-Common-Denominator-Step-16-Version-2.jpg\/v4-460px-Find-the-Least-Common-Denominator-Step-16-Version-2.jpg","bigUrl":"\/images\/thumb\/9\/90\/Find-the-Least-Common-Denominator-Step-16-Version-2.jpg\/aid2948791-v4-728px-Find-the-Least-Common-Denominator-Step-16-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    To determine the multiple needed to make the denominators equal, divide the LCD you determined by the original denominator. Multiply the numerator and the denominator of each fraction by this number. The denominators should now both be equal to the LCD.
    • Example: 60/4 = 15; 60/5 = 12; 60/12 = 5
    • 15 * (1/4) = 15/60; 12 * (1/5) = 12/60; 5 * (1/12) = 5/60
    • 15/60 + 12/60 + 5/60
  7. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/c\/c6\/Find-the-Least-Common-Denominator-Step-17-Version-2.jpg\/v4-460px-Find-the-Least-Common-Denominator-Step-17-Version-2.jpg","bigUrl":"\/images\/thumb\/c\/c6\/Find-the-Least-Common-Denominator-Step-17-Version-2.jpg\/aid2948791-v4-728px-Find-the-Least-Common-Denominator-Step-17-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    With the LCD found, you should be able to add and subtract the fractions as usual. Remember to simplify the fraction at the end, if possible.
    • Example: 15/60 + 12/60 + 5/60 = 32/60 = 8/15
    8. Advertisement
Method 4
Method 4 of 4:

Working with Integers and Mixed Numbers [13]

PDF download Download Article
  1. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/a\/a7\/Find-the-Least-Common-Denominator-Step-18-Version-2.jpg\/v4-460px-Find-the-Least-Common-Denominator-Step-18-Version-2.jpg","bigUrl":"\/images\/thumb\/a\/a7\/Find-the-Least-Common-Denominator-Step-18-Version-2.jpg\/aid2948791-v4-728px-Find-the-Least-Common-Denominator-Step-18-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    Convert mixed numbers into improper fractions by multiplying the integer by the denominator and adding the numerator to the product. Convert integers into improper fractions by placing the integer over a denominator of “1.”
    • Example: 8 + 2 1/4 + 2/3
    • 8 = 8/1
    • 2 1/4; 2 * 4 + 1 = 8 + 1 = 9; 9/4
    • Rewritten equation: 8/1 + 9/4 + 2/3
  2. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/4\/45\/Find-the-Least-Common-Denominator-Step-19-Version-2.jpg\/v4-460px-Find-the-Least-Common-Denominator-Step-19-Version-2.jpg","bigUrl":"\/images\/thumb\/4\/45\/Find-the-Least-Common-Denominator-Step-19-Version-2.jpg\/aid2948791-v4-728px-Find-the-Least-Common-Denominator-Step-19-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    Implement any of the methods used for finding the LCD of common fractions, as explained in the previous method sections. Note that for this example, we will be using the “listing multiples” method, in which a list of multiples is created for each denominator and the LCD is identified from these lists. [14]
    • Note that you do not need to create a list of multiples for 1 since any number multiplied by 1 equals itself; in other words, every number is a multiple of 1 .
    • Example: 4 * 1 = 4; 4 * 2 = 8; 4 * 3 = 12 ; 4 * 4 = 16; etc.
    • 3 * 1 = 3; 3 * 2 = 6; 3 * 3 = 9; 3 * 4 = 12 ; etc.
    • The LCD = 12
  3. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/5\/5e\/Find-the-Least-Common-Denominator-Step-20-Version-2.jpg\/v4-460px-Find-the-Least-Common-Denominator-Step-20-Version-2.jpg","bigUrl":"\/images\/thumb\/5\/5e\/Find-the-Least-Common-Denominator-Step-20-Version-2.jpg\/aid2948791-v4-728px-Find-the-Least-Common-Denominator-Step-20-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    Instead of multiplying the denominator alone, you must multiply the entire fraction by the digit required for changing the original denominator into the LCD.
    • Example: (12/12) * (8/1) = 96/12; (3/3) * (9/4) = 27/12; (4/4) * (2/3) = 8/12
    • 96/12 + 27/12 + 8/12
  4. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/4\/4b\/Find-the-Least-Common-Denominator-Step-21.jpg\/v4-460px-Find-the-Least-Common-Denominator-Step-21.jpg","bigUrl":"\/images\/thumb\/4\/4b\/Find-the-Least-Common-Denominator-Step-21.jpg\/aid2948791-v4-728px-Find-the-Least-Common-Denominator-Step-21.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    With the LCD determined and the original equation changed to reflect the LCD, you should be able to add and subtract without difficulty. Remember to simplify the fraction at the end, if possible. [15]
    • Example: 96/12 + 27/12 + 8/12 = 131/12 = 10 11/12
    5. Advertisement

Practice Problems and Answers

Expert Q&A

Search
Add New Question
  • Question
    How do you find the LCD of two fractions?
    Mario Banuelos, PhD
    Associate Professor of Mathematics
    Mario Banuelos is an Associate Professor of Mathematics at California State University, Fresno. With over eight years of teaching experience, Mario specializes in mathematical biology, optimization, statistical models for genome evolution, and data science. Mario holds a BA in Mathematics from California State University, Fresno, and a Ph.D. in Applied Mathematics from the University of California, Merced. Mario has taught at both the high school and collegiate levels.
    Mario Banuelos, PhD
    Associate Professor of Mathematics
    Expert Answer
    One way to do this is to write out all of the multiples of both denominators, then see where they match for the first time. You can also factor both the denominators and see if there are any common factors. If they do share common factors, the ones they do not have in common will give you insight into how to get the least common denominator.
    Thanks! We're glad this was helpful.
    Thank you for your feedback.
    If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
    Yes No
    Not Helpful 0 Helpful 1
  • Question
    What is the LCD of 1/4 and 3/8?
    Community Answer
    First, you must see what lowest number that both 4 and 8 will go into evenly. Since four can go evenly into 8, and 8 goes into itself evenly, then LCD of these two fractions is 8.
    Thanks! We're glad this was helpful.
    Thank you for your feedback.
    If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
    Yes No
    Not Helpful 7 Helpful 24
  • Question
    How do I subtract 4/5 from 8/10?
    Donagan
    Top Answerer
    Express both fractions with the same denominator. 4/5 is the equivalent of 8/10. 8/10 - 8/10 equals zero.
    Thanks! We're glad this was helpful.
    Thank you for your feedback.
    If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
    Yes No
    Not Helpful 7 Helpful 17
See more answers
Ask a Question
200 characters left
Include your email address to get a message when this question is answered.
Submit
      Advertisement

      Tips

      Submit a Tip
      All tip submissions are carefully reviewed before being published
      Name
      Please provide your name and last initial
      Submit
      Thanks for submitting a tip for review!

      Things You'll Need

      • Pencil
      • Paper
      • Calculator (optional)

      You Might Also Like

      Simple Ways to Find the Greatest Common Factor (GCF) of Numbers
      How to
      Find the Least Common Multiple of Two Numbers
      How to
      Order Fractions (with Examples)
      How to
      Find the Greatest Common Divisor of Two Integers
      Easy-to-Follow Methods for Adding Fractions
      How Do I Measure ¾ Cup?
      How to
      Multiply Fractions With Whole Numbers
      How to
      Divide Mixed Fractions
      How to
      Divide Fractions by a Whole Number
      How to
      Divide Fractions by Fractions
      How to
      Type Fractions
      How to
      Simplify Complex Fractions
      How to
      Add Fractions With Unlike Denominators
      How to
      Convert Improper Fractions Into Mixed Numbers
      Advertisement

      References

      1. ↑ https://www.mathsisfun.com/definitions/least-common-denominator.html
      2. ↑ Mario Banuelos, PhD. Associate Professor of Mathematics. Expert Interview. 11 December 2021.
      3. ↑ Mario Banuelos, PhD. Associate Professor of Mathematics. Expert Interview. 11 December 2021.
      4. ↑ https://www.mathsisfun.com/least-common-denominator.html
      5. ↑ https://www.mathsisfun.com/least-common-denominator.html
      6. ↑ http://www.aaamath.com/fra66jx2.htm
      7. ↑ https://www.mathsisfun.com/greatest-common-factor.html
      8. ↑ https://www.calculatorsoup.com/calculators/math/lcm.php
      9. ↑ https://www.calculator.net/lcm-calculator.html
      1. ↑ https://www.mathsisfun.com/prime_numbers.html
      2. ↑ https://math.libretexts.org/Bookshelves/PreAlgebra/Book%3A_Prealgebra_(OpenStax)/02%3A_Introduction_to_the_Language_of_Algebra/2.10%3A_Prime_Factorization_and_the_Least_Common_Multiple_(Part_2)
      3. ↑ https://math.libretexts.org/Bookshelves/PreAlgebra/Book%3A_Prealgebra_(OpenStax)/02%3A_Introduction_to_the_Language_of_Algebra/2.10%3A_Prime_Factorization_and_the_Least_Common_Multiple_(Part_2)
      4. ↑ http://www.calculatorsoup.com/calculators/math/lcd.php#.Ua0eFkDryj4
      5. ↑ https://www.calculatorsoup.com/calculators/math/lcd.php
      6. ↑ https://www.georgebrown.ca/sites/default/files/uploadedfiles/tlc/_documents/Adding_and_Subtracting_Mixed_Numbers_and_Improper_Fractions.pdf

      About This Article

      Article Summary X

      One way to find the least common denominator (LCD) of two or more fractions is by listing the factors of each denominator, which are all of the whole numbers that divide evenly into that number. Then, identify the greatest common factor between the two denominators. To use this number to find the LCD, multiply the two denominators together and divide that number by the greatest common factor. For example, for ⅜ and 5/12, the greatest common factor is 4, and the two denominators multiplied are 96. 96 divided by four is 24, which is the LCD. If you want to learn how to find the LCD using prime numbers, keep reading the article!

      Did this summary help you?
      In other languages
      Thanks to all authors for creating a page that has been read 773,442 times.

      Reader Success Stories

      • Logan Gomez

        Jan 24, 2018

        "I learned how to find the least common denominator. I needed to learn that information for my university homework."
      More reader stories Hide reader stories
      Share your story

      Did this article help you?

      Advertisement