What is the least common multiple of 8 and 15?

• A. 60
• B. 90
• C. 120
• D. 240

Answer: (C)

Finding the least common multiple means finding the smallest positive number that is divisible by both numbers. Do this by prime factorization: 8 is 2^3, and 15 is 3 × 5. To be divisible by both, a common multiple must include each prime at its highest power that appears in either factor: 2^3, 3, and 5. Multiply them together: 2^3 × 3 × 5 = 8 × 15 = 120. That number contains all the necessary prime factors and is the smallest such product, so it is the least common multiple. You can also verify by listing multiples: the first shared multiple of 8 and 15 is 120. Therefore, the least common multiple is 120.