The product of two numbers is 216 and their HCF is 6 . Find the lcm of two number.

Options

A. 52
B. 46
C. 34
D. 36

Answer

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

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Product of the two numbers (n1 and n2) = 216
- HCF (Highest Common Factor) of n1 and n2 = 6

2. **Use the Relationship Between Product, HCF, and LCM:**
- The relationship is given by the formula:
\[ \text{Product of two numbers} = \text{HCF} \times \text{LCM} \]
- In this case, we can express it as:
\[ n1 \times n2 = \text{HCF} \times \text{LCM} \]

3. **Substitute the Known Values:**
- Substitute the values we have into the equation:
\[ 216 = 6 \times \text{LCM} \]

4. **Solve for LCM:**
- To find the LCM, we can rearrange the equation:
\[ \text{LCM} = \frac{216}{6} \]
- Now, perform the division:
\[ \text{LCM} = 36 \]

5. **Conclusion:**
- Therefore, the LCM of the two numbers is **36**.