What is the least common multiple (LCM) of 6 and 8?

To find the least common multiple (LCM) of two numbers, such as 6 and 8, we begin by determining the prime factorization of each number.

The prime factorization of 6 is:

• 6 = 2 × 3

The prime factorization of 8 is:

• 8 = 2 × 2 × 2, or 2^3

To find the LCM, we take the highest power of each prime that appears in the factorizations. In this case, we have:

• For the prime number 2: the highest power is 2^3 (from 8).

• For the prime number 3: the highest power is 3^1 (from 6).

Now we multiply these together to get the LCM:

• LCM = 2^3 × 3^1 = 8 × 3 = 24.

Thus, the least common multiple of 6 and 8 is 24. This indicates that 24 is the smallest number that both 6 and 8 can divide without leaving a remainder, confirming that it is the correct answer.