Question

Find the least common multiple.
12 and 5

Answer 1

To find the least common multiple (LCM) of 12 and 5, we can use the following steps:

1. **List the prime factors of each number**:
- The prime factorization of 12 is \(2^2 \times 3^1\).
- The prime factorization of 5 is \(5^1\).

2. **Identify all the prime factors**:
- The unique prime factors from both numbers are 2, 3, and 5.

3. **Take the highest power of each prime factor**:
- For 2, the highest power is \(2^2\) (from 12).
- For 3, the highest power is \(3^1\) (from 12).
- For 5, the highest power is \(5^1\) (from 5).

4. **Multiply these together to get the LCM**:
\[
LCM = 2^2 \times 3^1 \times 5^1 = 4 \times 3 \times 5
\]

5. **Calculate the product**:
\[
4 \times 3 = 12
\]
\[
12 \times 5 = 60
\]

Thus, the least common multiple of 12 and 5 is **60**.