What is the least common multiple of 6 and 8?

What is the least common multiple of 6 and 8?

• A. 6
• B. 8
• C. 24
• D. 12

Answer: (C)

Finding the least common multiple means identifying the smallest number that is a multiple of both numbers. A solid way to see this is through prime factorization: 6 breaks down to 2 × 3, and 8 breaks down to 2^3. For the LCM, take each prime factor to the highest power it appears in either factorization. That gives 2^3 × 3 = 8 × 3 = 24. This number is divisible by both 6 and 8, and no smaller positive number serves as a common multiple for both. You can confirm by listing multiples: 6’s multiples are 6, 12, 18, 24, … and 8’s multiples are 8, 16, 24, …, with the first common one being 24.

Finding the least common multiple means identifying the smallest number that is a multiple of both numbers. A solid way to see this is through prime factorization: 6 breaks down to 2 × 3, and 8 breaks down to 2^3. For the LCM, take each prime factor to the highest power it appears in either factorization. That gives 2^3 × 3 = 8 × 3 = 24. This number is divisible by both 6 and 8, and no smaller positive number serves as a common multiple for both. You can confirm by listing multiples: 6’s multiples are 6, 12, 18, 24, … and 8’s multiples are 8, 16, 24, …, with the first common one being 24.