What is the least common multiple (LCM) of 4 and 6?

To find the least common multiple (LCM) of two numbers, you need to determine the smallest multiple that both numbers share. For 4 and 6, you can list their multiples or use prime factorization.

The multiples of 4 are: 4, 8, 12, 16, 20, 24, ...

The multiples of 6 are: 6, 12, 18, 24, ...

The smallest number that appears in both lists of multiples is 12, making it the least common multiple of 4 and 6.

In terms of prime factorization, you can express 4 as (2^2) and 6 as (2^1 \times 3^1). To find the LCM, take the highest power of each prime that appears in the factorizations. This gives you (2^2) from 4 and (3^1) from 6. When you multiply these together, you get (2^2 \times 3^1 = 4 \times 3 = 12).

Therefore, the LCM of 4 and 6 is 12, confirming that the choice of 12 is correct