The HCF and LCM of two numbers are 16 and 160 respectively. If first number is 32, then the second number is

Options

A. 48
B. 80
C. 96
D. 112

Answer

To find the second number given the HCF, LCM, and the first number, we can use the relationship between these values. The formula we will use is:

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

### Step-by-step Solution:

1. **Identify the given values**:
- HCF = 16
- LCM = 160
- First Number = 32

2. **Set up the equation**:
Let the second number be \( x \). According to the formula:
\[ 16 \times 160 = 32 \times x \]

3. **Calculate the left side of the equation**:
\[ 16 \times 160 = 2560 \]

4. **Substitute this value back into the equation**:
\[ 2560 = 32 \times x \]

5. **Solve for \( x \)**:
To find \( x \), divide both sides by 32:
\[ x = \frac{2560}{32} \]

6. **Calculate the division**:
\[ x = 80 \]

7. **Conclusion**:
The second number is \( 80 \).

### Final Answer:
The second number is **80**.

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