Question

Find the least common multiple of 7 and 12.(1 point)

Answer 1

To find the least common multiple (LCM) of 7 and 12, we can use the prime factorization method or the relationship between LCM and the greatest common divisor (GCD).

1. **Prime Factorization**:
- The prime factors of 7 are \(7^1\).
- The prime factors of 12 are \(2^2 \times 3^1\).

2. **Identify the highest powers of all prime factors**:
- The primes involved are 2, 3, and 7.
- The highest power of 2: \(2^2\)
- The highest power of 3: \(3^1\)
- The highest power of 7: \(7^1\)

3. **Multiply these together**:
\[
\text{LCM} = 2^2 \times 3^1 \times 7^1 = 4 \times 3 \times 7
\]

- First calculate \(4 \times 3 = 12\).
- Then calculate \(12 \times 7 = 84\).

Therefore, the least common multiple of 7 and 12 is \(84\).