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

Responses

A 18

B 24

C 27

D 32

1 answer

To find the least common multiple (LCM) of the numbers 6 and 8, we can use the prime factorization method.

  1. Prime factorization:

    • The prime factorization of 6 is \(2^1 \times 3^1\).
    • The prime factorization of 8 is \(2^3\).
  2. LCM calculation:

    • For each prime factor, take the highest power that appears in the factorizations.
    • For the prime number 2, the highest power is \(2^3\).
    • For the prime number 3, the highest power is \(3^1\).
  3. Calculating the LCM: \[ LCM = 2^3 \times 3^1 = 8 \times 3 = 24 \]

Thus, the LCM of 6 and 8 is 24.

So the answer is B. 24.