The HCF of two numbers is 6 and their LCM is 432. If one of the number is 48, the other number is:

Options

A. 42
B. 27
C. 52
D. 54

Explanation

To find the other number given that the HCF of two numbers is 6, their LCM is 432, and one of the numbers is 48, we can use the relationship between HCF, LCM, and the two numbers.

### Step-by-step Solution:

1. **Understand the relationship**:
The relationship between the two numbers (let's call them \( a \) and \( b \)), their HCF (Highest Common Factor), and their LCM (Lowest Common Multiple) is given by the formula:
\[ a \times b = \text{HCF} \times \text{LCM} \]

2. **Substitute the known values**:
Here, we know:
- \( \text{HCF} = 6 \)
- \( \text{LCM} = 432 \)
- One of the numbers \( a = 48 \)
We need to find the other number \( b \).

Plugging these values into the formula gives:
\[ 48 \times b = 6 \times 432 \]

3. **Calculate the right side**:
First, calculate \( 6 \times 432 \):
\[ 6 \times 432 = 2592 \]

4. **Set up the equation**:
Now we have:
\[ 48 \times b = 2592 \]

5. **Solve for \( b \)**:
To find \( b \), divide both sides of the equation by 48:
\[ b = \frac{2592}{48} \]

6. **Perform the division**:
Now, calculate \( \frac{2592}{48} \):
- First, simplify \( 2592 \div 48 \):
\[ 2592 \div 48 = 54 \]

7. **Conclusion**:
Therefore, the other number \( b \) is:
\[ b = 54 \]

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