The product of two numbers is 180 and their L.C.M. is 36. Find the H.C.F.

Options

A. 5
B. 125
C. 60
D. 150

Answer

To find the H.C.F. (Highest Common Factor) of two numbers given their product and L.C.M. (Lowest Common Multiple), we can use the relationship between these three quantities. The formula we will use is:

**Product of two numbers = LCM × HCF**

Given:
- Product of two numbers (A × B) = 180
- LCM = 36

We need to find the HCF.

### Step-by-step Solution:

1. **Write down the formula**:
\[ A \times B = \text{LCM} \times \text{HCF} \]

2. **Substitute the known values into the formula**:
\[ 180 = 36 \times \text{HCF} \]

3. **Rearrange the equation to solve for HCF**:
\[ \text{HCF} = \frac{180}{36} \]

4. **Perform the division**:
\[ \text{HCF} = 5 \]

Thus, the H.C.F. of the two numbers is **5**.