What is the least common multiple of 9 and 12?

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Multiple Choice

What is the least common multiple of 9 and 12?

Explanation:
The concept here is finding the smallest number that is a multiple of both numbers. Break each into prime factors: 9 = 3^2 and 12 = 2^2 × 3. To get the least common multiple, take each prime factor to the highest power it appears in either factor: 2^2 and 3^2. Multiply them to get 2^2 × 3^2 = 4 × 9 = 36. This number is divisible by both 9 and 12, and no smaller number shares that property. For example, 18 equals 2 × 3^2 (missing a 2^2 factor), so it isn’t divisible by 12; 72 has extra factors (2^3), so it’s not the smallest; and 9 isn’t divisible by 12. Thus, the least common multiple is 36.

The concept here is finding the smallest number that is a multiple of both numbers. Break each into prime factors: 9 = 3^2 and 12 = 2^2 × 3. To get the least common multiple, take each prime factor to the highest power it appears in either factor: 2^2 and 3^2. Multiply them to get 2^2 × 3^2 = 4 × 9 = 36. This number is divisible by both 9 and 12, and no smaller number shares that property. For example, 18 equals 2 × 3^2 (missing a 2^2 factor), so it isn’t divisible by 12; 72 has extra factors (2^3), so it’s not the smallest; and 9 isn’t divisible by 12. Thus, the least common multiple is 36.

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