If the product of two number is 2664 and their LCM is 74 then their HCF is :

Options

A. 34
B. 36
C. 64
D. 35

Answer

To find the HCF (Highest Common Factor) of two numbers given their product and LCM (Least Common Multiple), we can use the relationship between these quantities. The formula we will use is:

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

### Step-by-Step Solution:

1. **Identify the given values**:
- Product of the two numbers (A × B) = 2664
- LCM of the two numbers = 74

2. **Use the formula**:
According to the formula, we have:
\[ A \times B = \text{LCM} \times \text{HCF} \]
Substituting the known values:
\[ 2664 = 74 \times \text{HCF} \]

3. **Rearranging the equation to find HCF**:
To find HCF, we can rearrange the equation:
\[ \text{HCF} = \frac{2664}{74} \]

4. **Perform the division**:
Now, we will calculate:
\[ \text{HCF} = \frac{2664}{74} = 36 \]

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

### Final Answer:
The HCF is **36**.