The product of two numbers is `396 xx 576` and their LCM is 6336. Find their HCF:

Options

A. 36
B. 34
C. 63
D. 43

Answer

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

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

Given:
- Product of the two numbers = \(396 \times 576\)
- LCM = \(6336\)

### Step-by-step Solution:

1. **Calculate the Product of the Two Numbers**:
\[ \text{Product} = 396 \times 576 \]

Let's calculate this:
\[ 396 \times 576 = 228576 \]

2. **Use the Relationship to Find HCF**:
According to the formula:
\[ \text{HCF} = \frac{\text{Product of the two numbers}}{\text{LCM}} \]

Substitute the values we have:
\[ \text{HCF} = \frac{228576}{6336} \]

3. **Perform the Division**:
Now, we need to divide \(228576\) by \(6336\):
\[ \text{HCF} = 36 \]

### Final Answer:
The HCF of the two numbers is \(36\).