Question

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

A 18

B 24

C 27

D 32

Answer 1

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**.