Question

Find the least common multiple of 12 and 27

Answer 1

To find the least common multiple (LCM) of 12 and 27, we can use the prime factorization method.

1. **Prime factorization:**
- The prime factorization of 12 is:
\[
12 = 2^2 \times 3^1
\]
- The prime factorization of 27 is:
\[
27 = 3^3
\]

2. **Identify the highest power of each prime factor:**
- For the prime factor 2, the highest power in the factorizations is \(2^2\) from 12.
- For the prime factor 3, the highest power is \(3^3\) from 27.

3. **Multiply the highest powers together to find the LCM:**
\[
\text{LCM} = 2^2 \times 3^3
\]
- Calculate \(2^2\):
\[
2^2 = 4
\]
- Calculate \(3^3\):
\[
3^3 = 27
\]
- Now multiply these results:
\[
\text{LCM} = 4 \times 27 = 108
\]

Therefore, the least common multiple of 12 and 27 is \(\boxed{108}\).