What is the least common multiple of 6 and 8?

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Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

What is the least common multiple of 6 and 8?

Explanation:
Finding the least common multiple means finding the smallest number that is divisible by both numbers. Do this by prime factorization: 6 breaks down to 2 × 3, and 8 breaks down to 2^3. Take the highest power of each prime that appears in either factorization: 2^3 and 3. Multiply them together: 2^3 × 3 = 8 × 3 = 24. So 24 is divisible by both 6 (24 ÷ 6 = 4) and 8 (24 ÷ 8 = 3), and there isn’t a smaller positive number that works. For reference, 12 isn’t divisible by 8, 16 isn’t divisible by 6, and 48 is bigger than 24.

Finding the least common multiple means finding the smallest number that is divisible by both numbers. Do this by prime factorization: 6 breaks down to 2 × 3, and 8 breaks down to 2^3. Take the highest power of each prime that appears in either factorization: 2^3 and 3. Multiply them together: 2^3 × 3 = 8 × 3 = 24. So 24 is divisible by both 6 (24 ÷ 6 = 4) and 8 (24 ÷ 8 = 3), and there isn’t a smaller positive number that works. For reference, 12 isn’t divisible by 8, 16 isn’t divisible by 6, and 48 is bigger than 24.

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