What is the least common multiple of 6 and 8?

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Multiple Choice

What is the least common multiple of 6 and 8?

Explanation:
The least common multiple is the smallest positive number that is a multiple of both numbers. List their multiples and find the first one that appears in both lists: multiples of 6 are 6, 12, 18, 24, … and multiples of 8 are 8, 16, 24, 32, …. The first common multiple is 24, so the LCM is 24. You can also do it with prime factors: 6 = 2 × 3 and 8 = 2^3, so take each prime to its highest power: 2^3 × 3 = 8 × 3 = 24. The other numbers don’t work because they’re not divisible by both numbers (12 isn’t divisible by 8, 16 isn’t divisible by 6) or they’re larger than the smallest common multiple (48).

The least common multiple is the smallest positive number that is a multiple of both numbers. List their multiples and find the first one that appears in both lists: multiples of 6 are 6, 12, 18, 24, … and multiples of 8 are 8, 16, 24, 32, …. The first common multiple is 24, so the LCM is 24. You can also do it with prime factors: 6 = 2 × 3 and 8 = 2^3, so take each prime to its highest power: 2^3 × 3 = 8 × 3 = 24. The other numbers don’t work because they’re not divisible by both numbers (12 isn’t divisible by 8, 16 isn’t divisible by 6) or they’re larger than the smallest common multiple (48).

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