Which concept is defined as the smallest number that is a common multiple of two or more numbers?

• A. GCF
• B. Prime number
• C. LCM
• D. Compatible numbers

Answer: (C)

The concept being tested is the least common multiple: the smallest number that can be evenly divided by each of the given numbers. To see it, look at multiples of the two numbers and find the first one they share. For example, multiples of six are 6, 12, 18, 24, … and multiples of eight are 8, 16, 24, …; the first common multiple is 24, so 24 is the least common multiple. You can also find it by prime factorization: 6 = 2 × 3 and 8 = 2^3; take the highest powers of all primes involved, giving 2^3 × 3 = 24. This idea is different from the greatest common factor, which is the largest number that divides both numbers. A prime number is simply a number with exactly two divisors, not about common multiples, and compatible numbers are a mental-math estimation aid, not the concept of common multiples.