List the factors of the denominators of two fractions. Factors are the set of all numbers that can divide evenly into another number. For example, the factors of the denominator of 3/20 include 1, 2, 4, 5, 10 and 20. The factors of the denominator of 4/15 include 1, 3, 5 and 15.
Find the greatest common factor of the two denominators. This is the largest number that divides evenly into both denominators. In this example, the denominator's greatest common factor is 5.
Multiply the denominators together. In this example, 20 multiplied by 15 equals 300.
Divide the product of the two denominators by their greatest common factor to calculate the common denominator. In this example, 300 divided by 5 equals 60.
Divide the amount by the original denominators. In this example, 60 divided by 20 equals 3, and 60 divided by 15 equals 4.
Multiply the fraction's numerators by the quotients calculated with their respective denominators. In this example, multiplying 3 by 3 results in 9, and multiplying 4 by 4 results in 16.
Write the products from the prior step as the numerators of two separate fractions, with each being placed over the common denominator from Step 4. Concluding this example, the two fractions 3/20 and 4/15 become 9/60 and 16/60.