What is the least common denominator of 3/4 and 1/5?

• A. 10
• B. 20
• C. 4
• D. 5

Answer: (B)

To add or compare fractions you need a common denominator—the smallest number that both denominators divide into evenly. For 3/4 and 1/5, the denominators are 4 and 5. The multiples of 4 are 4, 8, 12, 16, 20, ... and the multiples of 5 are 5, 10, 15, 20, ... The first number that appears in both lists is 20, so 20 is the least common denominator. Using this denominator, 3/4 becomes 15/20 and 1/5 becomes 4/20, which makes addition or comparison straightforward. The other options don’t work as common denominators: 4 and 5 are the original denominators, 10 isn’t a multiple of 4, so it isn’t a common denominator, while 20 is the smallest that works.