The smallest number that is completely divisibly by 6. 8. 12 and 16 is-
A. 48
B. 24
C. 64
D. 80

Options

A. C
B. B
C. D
D. A

Answer

To find the smallest number that is completely divisible by 6, 8, 12, and 16, we need to calculate the Least Common Multiple (LCM) of these numbers.

### Step-by-Step Solution:

1. **List the Numbers**: We have the numbers 6, 8, 12, and 16.

2. **Prime Factorization**:
- 6 = 2 × 3
- 8 = 2^3
- 12 = 2^2 × 3
- 16 = 2^4

3. **Identify the Highest Powers of Each Prime**:
- For the prime number 2, the highest power in the factorizations is 2^4 (from 16).
- For the prime number 3, the highest power is 3^1 (from 6 and 12).

4. **Calculate the LCM**:
- LCM = 2^4 × 3^1
- LCM = 16 × 3 = 48

5. **Conclusion**: The smallest number that is completely divisible by 6, 8, 12, and 16 is **48**.

### Answer:
The correct option is **A. 48**.