The HCF and LCM of two numbers are 4 and 48 respectively. If one of these numbers is 12, the second number is

Options

A. 16
B. 12
C. 8
D. 4

Answer

To find the second number when the HCF and LCM of two numbers are given, we can use the relationship between HCF, LCM, and the two numbers. The formula is:

\[ \text{HCF} \times \text{LCM} = \text{Product of the two numbers} \]

### Step-by-Step Solution:

1. **Identify the given values:**
- HCF = 4
- LCM = 48
- One of the numbers (let's call it \( a \)) = 12

2. **Use the formula:**
\[ \text{HCF} \times \text{LCM} = a \times b \]
where \( b \) is the second number we need to find.

3. **Substitute the known values into the formula:**
\[ 4 \times 48 = 12 \times b \]

4. **Calculate the left side:**
\[ 4 \times 48 = 192 \]
So, we have:
\[ 192 = 12 \times b \]

5. **Solve for \( b \):**
To find \( b \), divide both sides by 12:
\[ b = \frac{192}{12} \]

6. **Calculate \( b \):**
\[ b = 16 \]

### Conclusion:
The second number is **16**.