What is the least common multiple of 9 and 12?

What is the least common multiple of 9 and 12?

• A. 18
• B. 24
• C. 72
• D. 36

Answer: (D)

Finding the least common multiple means finding the smallest number that both 9 and 12 divide into. Use prime factors: 9 is 3 squared, 12 is 2 squared times 3. To be divisible by both, include each prime factor at its highest needed power: 2^2 and 3^2. Multiply them to get 4 × 9 = 36. So 36 is the smallest number that is a multiple of both. 18 isn’t divisible by 4, so it’s not a multiple of 12. 24 has 2^3 but only one 3, so it’s not divisible by 9. 72 works too, but it’s larger than the smallest.

Finding the least common multiple means finding the smallest number that both 9 and 12 divide into. Use prime factors: 9 is 3 squared, 12 is 2 squared times 3. To be divisible by both, include each prime factor at its highest needed power: 2^2 and 3^2. Multiply them to get 4 × 9 = 36. So 36 is the smallest number that is a multiple of both.

18 isn’t divisible by 4, so it’s not a multiple of 12. 24 has 2^3 but only one 3, so it’s not divisible by 9. 72 works too, but it’s larger than the smallest.