Which statement correctly defines the least common multiple (LCM)?

Which statement correctly defines the least common multiple (LCM)?

• A. The greatest factor that two numbers have in common
• B. The smallest multiple (other than zero) that two or more numbers have in common
• C. The largest multiple that two numbers have in common
• D. A factor of two numbers

Answer: (B)

The least common multiple is the smallest positive number that is a multiple of each number. For two numbers, this means the smallest positive common multiple. For instance, the LCM of 4 and 6 is 12, since 12 is divisible by both 4 and 6 and there’s no smaller positive number with that property. The other statements refer to different ideas: the greatest common divisor is the largest number that divides both, not a multiple; there is no largest common multiple because multiples keep increasing; a common factor is a divisor, not a multiple.

The least common multiple is the smallest positive number that is a multiple of each number. For two numbers, this means the smallest positive common multiple. For instance, the LCM of 4 and 6 is 12, since 12 is divisible by both 4 and 6 and there’s no smaller positive number with that property. The other statements refer to different ideas: the greatest common divisor is the largest number that divides both, not a multiple; there is no largest common multiple because multiples keep increasing; a common factor is a divisor, not a multiple.