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.