What is the LCM of 4, 9, 12?

To find the Least Common Multiple (LCM) of 4, 9, and 12, follow these steps:

1. **Prime factorize each number**:
- 4 = 2 × 2 = \(2^2\)
- 9 = 3 × 3 = \(3^2\)
- 12 = 2 × 2 × 3 = \(2^2 × 3\)

2. **Identify the highest powers of all prime factors**:
- For the factor 2: The highest power is \(2^2\) (from 4 and 12).
- For the factor 3: The highest power is \(3^2\) (from 9).

3. **Multiply these highest powers**:
- LCM = \(2^2 × 3^2\) = 4 × 9 = 36

4. **Verify**:
- Check if 36 is divisible by each of the original numbers:
- 36 ÷ 4 = 9 (an integer, so divisible by 4)
- 36 ÷ 9 = 4 (an integer, so divisible by 9)
- 36 ÷ 12 = 3 (an integer, so divisible by 12)

Thus, the LCM of 4, 9, and 12 is **36**.