# How to Express Fractions in Terms of the Least Common Multiple

By Chance E. Gartneer
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Fractions must have the same denominators (the bottom number) before you can add or subtract them. A denominator shared between fractions is called a common denominator. The smallest possible common denominator is called the least common denominator. The least common denominator is the least common multiple of the original denominators, or the smallest number other than zero that is a multiple of both. By finding the denominators' least common multiple, you can change the fractions into a solvable expression.

Calculate the first five multiples of the first fraction's denominator. For a example, let the first fraction be 1/4 --- the first five multiples of 4 are 4, 8, 12, 16 and 20.

Calculate the first five multiples of the second fraction's denominator. For example, let the second fraction be 1/6 --- the first five multiples of 6 are 6, 12, 18, 24 and 30.

Find the smallest number that appears in both lists of the denominators' multiples. This is the least common multiple. In the previous examples, 12 is the least common multiple of 4 and 6.

Rename the fractions so they have the same denominators. Divide the least common multiple by the first fraction's denominator, multiply the numerator by that quotient, then write the product over the least common multiple to rename the first fraction. In this example, dividing 12 by 4 equals 3, and multiplying 1 by 3 equals 3 --- the fraction 1/4 becomes 3/12.

Divide the least common multiple by the second fraction's denominator, multiply the numerator by that quotient, and write the product over the least common multiple to rename the second fraction. In this example, dividing 12 by 6 equals 2, and multiplying 1 by 2 equals 2 --- the fraction 1/6 becomes 2/12.