The product of two numbers is 20736 and their HCF is 54. Find their LCM.

Options

A. 685
B. 468
C. 648
D. 384

Answer

To find the LCM of two numbers given their product and HCF, we can use the relationship:

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

Given:
- Product of two numbers = 20736
- HCF = 54

We need to find the LCM.

### Step-by-Step Solution:

1. **Use the formula**:
\[ \text{LCM} = \frac{\text{Product of two numbers}}{\text{HCF}} \]

2. **Substitute the known values**:
\[ \text{LCM} = \frac{20736}{54} \]

3. **Perform the division**:
- First, simplify the division:
\[ 20736 \div 54 \]

4. **Calculate the result**:
- Performing the division:
\[ 20736 \div 54 = 384 \]

5. **Conclusion**:
- Therefore, the LCM of the two numbers is:
\[ \text{LCM} = 384 \]

### Final Answer:
The LCM of the two numbers is **384**.

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