What is the least common multiple of 3 and 5?

What is the least common multiple of 3 and 5?

• A. 8
• B. 15
• C. 12
• D. 30

Answer: (B)

The least common multiple is the smallest number that is a multiple of both numbers. Since 3 and 5 have no common factors besides 1, their LCM is simply their product: 3 × 5 = 15. You can see this by listing multiples: multiples of 3 are 3, 6, 9, 12, 15, ... and multiples of 5 are 5, 10, 15, ... The first number that appears in both lists is 15, so 15 is the least common multiple. The other options don’t fit because they aren’t divisible by both numbers (8 isn’t divisible by 3 or 5; 12 isn’t divisible by 5; 30 is divisible by both but isn’t the smallest).

The least common multiple is the smallest number that is a multiple of both numbers. Since 3 and 5 have no common factors besides 1, their LCM is simply their product: 3 × 5 = 15. You can see this by listing multiples: multiples of 3 are 3, 6, 9, 12, 15, ... and multiples of 5 are 5, 10, 15, ... The first number that appears in both lists is 15, so 15 is the least common multiple. The other options don’t fit because they aren’t divisible by both numbers (8 isn’t divisible by 3 or 5; 12 isn’t divisible by 5; 30 is divisible by both but isn’t the smallest).