Q&A for How to Find the Least Common Denominator

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.

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.

Express both fractions with the same denominator. 4/5 is the equivalent of 8/10. 8/10 - 8/10 equals zero.

Change ½ to 3/6. Subtract 3/6 from 5/6. Then divide by ¼, which is the same as multiplying by 4.

The easiest way to do it is to multiply any two or three of those numbers and see if the product is also a multiple of each of the other numbers. If so, that's a common multiple. Then divide that number by any small number to see if there's a lower common multiple. In this case you'll find that the lowest common multiple is the full product of 7, 8, 9 and 10, which is 5,040.

Simply multiply the two fractions together (numerator times numerator, and denominator times denominator), reduce the fraction if possible, then put a 3 in front of the final fraction. The answer will be a mixed number. Thus: (7/9)(2/98) = 14 / 882 = 1/63. The answer is 3 1/63.

Multiply the two fractions together, then find the square root of the product: (1/16)(4/25) = 4/400 = 1/100. The square root of 1/100 is 1/10.

You multiply 14 by 4/7: (14/1)(4/7) = 56/7 = 8.

Multiply the smaller denominator (6) by various small integers (2, 3, 4, etc.) until you get a product that is also a multiple of the other denominator (9). Thus, 2x6=12, which is not a multiple of 9. 3x6=18, which is a multiple of 9. Therefore, 18 is the least common denominator of 5/6 and 2/9.

For ease, start the process with the two smallest denominators, here 16 and 18. Multiply them together: 16 x 18 = 288. Thus, 288 is evenly divisible by 16 and by 18. Divide 288 by the other denominator to see if it, too, divides evenly: 288 ÷ 24 = 12. Because it divides evenly (in other words, with a quotient that is a whole number), 288 is the smallest number evenly divisible by each of the denominators and is thus defined as the lowest (least) common denominator in this case.

12 x 2 = 24, and 8 x 3 = 24. 24 is the lowest number that is a multiple of both 8 and 12, so 24 is the LCD.

¼(2x - 1) = (2x - 1) / 4.

The LCD is 9 x 4 = 36. Nothing lower will work.

The LCD is 42 (6 x 7).

The lowest multiples of 12 are 24, 36, 48 and 60. The lowest multiples of 15 are 30, 45 and 60. The LCD is 60.

First simplify both expressions. 2 4/9 is 22/9. 22/9 x 611 = 13,442 / 9. That's the numerator (or the dividend). 5 3/4 is 23/4 or 69/12, and 1/3 is 4/12. 69/12 - 4/12 is 65/12. That's the denominator (or the divisor). So the simplified problem is 13,442 / 9 ÷ 65/12. The easiest thing to do here is to invert 65/12 and multiply: [13,442 / 9][12/65] = 161,304 / 585 = 275.733.

That's not an easy example for a beginning student because the number 26 is rather awkward. Let's take an easier example with denominators of 2, 3 and 5. The lowest multiples of 2 are 2, 4, 6, 8, 10, 12 14, 16, 18, 20, 22, 24, 26, 28 and 30. The lowest multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27 and 30. The lowest multiples of 5 are 5, 10, 15, 20, 25 and 30. So the lowest multiple common to all three denominators is 30. That's the LCD. In your more difficult example, you'd have to multiply the three denominators together to get a common multiple (which might or might not be the LCD).

If you factor both numbers you will find 63 = 21 * 3, and 84 = 21 * 4. Therefore, if you multiply the common factor 21 by the other factors, 3 and 4, you get 21*3*4 = 252, which equals both 63*4 and 84*3 and is the least common multiple of 63 and 84.

The LCD is 12. That's the lowest number that is evenly divisible by each of the denominators.

The least common denominator between 4 and 8 is 8. This is 6/8 + 7/8 = 13/8, which is 1 5/8. Your final answer is 1 5/8.

Once you've changed a denominator, you have to change the numerator, too, so that the value of the fraction remains the same. For example, if you're adding 1/3 + 2/5, the lowest common denominator is 15. So you change each denominator to 15. Now you change each numerator so that each fraction retains its value. First look at 1/3. You have to multiply that denominator by 5 in order to get the new denominator, so you also multiply the numerator by 5 to get the new numerator, and the new fraction is 5/15. Now look at 2/5. You have to multiply that denominator by 3 to get the new denominator. So you also have to multiply the old numerator by 3 to get the new numerator. The new fraction is 6/15. Then 1/3 + 2/5 = 5/15 + 6/15 = 11/15.