LCM and HCF of two numbers are 96 and 4, respectively. If one of the numbers is 32, then find the another number.

Options

A. 12
B. 16
C. 14
D. 18

Answer

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

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

Given:
- LCM = 96
- HCF = 4
- First Number = 32
- Second Number = ?

Let's denote the second number as \( x \).

### Step-by-step Solution:

1. **Write down the formula**:
\[ \text{LCM} \times \text{HCF} = \text{First Number} \times \text{Second Number} \]
Substituting the known values:
\[ 96 \times 4 = 32 \times x \]

2. **Calculate LCM multiplied by HCF**:
\[ 96 \times 4 = 384 \]
So, we have:
\[ 384 = 32 \times x \]

3. **Isolate \( x \)**:
To find \( x \), divide both sides by 32:
\[ x = \frac{384}{32} \]

4. **Perform the division**:
\[ x = 12 \]

5. **Conclusion**:
The other number is \( 12 \).

### Final Answer:
The other number is **12**.