What is the least common multiple of 6 and 8?

What is the least common multiple of 6 and 8?

• A. 12
• B. 18
• C. 30
• D. 24

Answer: (D)

Finding the least common multiple is about the smallest number that is a multiple of both numbers. A reliable way to find it is to use prime factorization: break each number into primes, take the highest power of each prime that appears, and multiply those together. For 6 and 8, factor them as 6 = 2 × 3 and 8 = 2^3. The combined factors take the highest powers: 2^3 and 3. Multiply them to get 2^3 × 3, which equals 24. This number is divisible by both 6 and 8 (24 ÷ 6 = 4 and 24 ÷ 8 = 3), so it is a common multiple, and any smaller candidate would miss either the factor of 3 or enough factors of 2. Checking the other options: a smaller number that is divisible by 6 but not by 8 wouldn’t qualify, and a number that isn’t divisible by 8 also wouldn’t qualify. Therefore, 24 is the smallest common multiple of 6 and 8.

Finding the least common multiple is about the smallest number that is a multiple of both numbers. A reliable way to find it is to use prime factorization: break each number into primes, take the highest power of each prime that appears, and multiply those together.

For 6 and 8, factor them as 6 = 2 × 3 and 8 = 2^3. The combined factors take the highest powers: 2^3 and 3. Multiply them to get 2^3 × 3, which equals 24. This number is divisible by both 6 and 8 (24 ÷ 6 = 4 and 24 ÷ 8 = 3), so it is a common multiple, and any smaller candidate would miss either the factor of 3 or enough factors of 2.

Checking the other options: a smaller number that is divisible by 6 but not by 8 wouldn’t qualify, and a number that isn’t divisible by 8 also wouldn’t qualify. Therefore, 24 is the smallest common multiple of 6 and 8.