The HCF of two numbers is 6 and their LCM is 108. If one of the numbers is 12, then the other is .
A.27
B. 54
C. 48
D. 36.

Options

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

Answer

To solve the problem, we can use the relationship between the Highest Common Factor (HCF), Lowest Common Multiple (LCM), and the two numbers. The formula is:

\[ \text{HCF} \times \text{LCM} = \text{First Number} \times \text{Second Number} \]

Given:
- HCF = 6
- LCM = 108
- First Number = 12
- Second Number = ?

We need to find the second number.

### Step-by-step Solution:

1. **Write down the formula**:
\[ \text{HCF} \times \text{LCM} = \text{First Number} \times \text{Second Number} \]

2. **Substitute the known values into the formula**:
\[ 6 \times 108 = 12 \times \text{Second Number} \]

3. **Calculate the left side**:
\[ 648 = 12 \times \text{Second Number} \]

4. **Isolate the Second Number**:
To find the Second Number, divide both sides by 12:
\[ \text{Second Number} = \frac{648}{12} \]

5. **Perform the division**:
\[ \text{Second Number} = 54 \]

Thus, the other number is **54**.

### Final Answer:
The other number is **B. 54**.