What is the least common multiple of 8 and 12?

The least common multiple (LCM) of 8 and 12 is the smallest positive integer that is a multiple of both 8 and 12.

Here's how to find it:

• Method 1: Listing multiples: List the multiples of 8 (8, 16, 24, 32, 40...) and the multiples of 12 (12, 24, 36...). The smallest number that appears in both lists is 24. Therefore, the LCM(8, 12) = 24.

• Method 2: Prime factorization:

  • Find the prime factorization of each number:
    • 8 = 2 x 2 x 2 = 2³
    • 12 = 2 x 2 x 3 = 2² x 3
  • Take the highest power of each prime factor present in the factorizations: The highest power of 2 is 2³ = 8, and the highest power of 3 is 3¹ = 3.
  • Multiply these highest powers together: 8 x 3 = 24. Therefore, the LCM(8, 12) = 24.

In short, the least common multiple of 8 and 12 is $\boxed{24}$.