The product of two numbers is 216. If the HCF is 6, then their LCM is:

Options

A. 72
B. 60
C. 48
D. 36

Answer

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

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

Given:
- Product of two numbers (N1 and N2) = 216
- HCF (N1, N2) = 6

We need to find the LCM (N1, N2).

### Step-by-step Solution:

1. **Write down the relationship**:
\[ N1 \times N2 = \text{HCF} \times \text{LCM} \]

2. **Substitute the known values**:
\[ 216 = 6 \times \text{LCM} \]

3. **Solve for LCM**:
To isolate LCM, divide both sides by 6:
\[ \text{LCM} = \frac{216}{6} \]

4. **Calculate the division**:
\[ \text{LCM} = 36 \]

Thus, the LCM of the two numbers is **36**.