Question

What is the least common multiple of 12 and 8?

Answer 1

To find the least common multiple (LCM) of 12 and 8, we can use the following method:

1. **Prime Factorization**:
- The prime factorization of 12 is \(2^2 \times 3^1\).
- The prime factorization of 8 is \(2^3\).

2. **Identify the Highest Power of Each Prime**:
- The prime factors involved are 2 and 3.
- For the prime number 2, the highest power between the factorizations is \(2^3\) (from 8).
- For the prime number 3, the highest power is \(3^1\) (from 12).

3. **Multiply the Highest Powers Together**:
\[
\text{LCM} = 2^3 \times 3^1 = 8 \times 3 = 24
\]

Thus, the least common multiple of 12 and 8 is \(\boxed{24}\).