Given that LCM (252,594)=8316. Find HCF (252,594).

Answer

To find the HCF (Highest Common Factor) of the numbers 252 and 594 given that their LCM (Lowest Common Multiple) is 8316, we can use the relationship between LCM, HCF, and the product of the two numbers.

### Step-by-Step Solution:

1. **Understand the Relationship**:
The relationship between LCM, HCF, and the two numbers is given by the formula:
\[ \text{LCM}(a, b) \times \text{HCF}(a, b) = a \times b \]
where \( a = 252 \) and \( b = 594 \).

2. **Substitute the Known Values**:
We know:
- \( \text{LCM}(252, 594) = 8316 \)
- \( a = 252 \)
- \( b = 594 \)

Plugging these values into the formula gives:
\[ 8316 \times \text{HCF}(252, 594) = 252 \times 594 \]

3. **Calculate the Product of the Two Numbers**:
Now, we need to calculate \( 252 \times 594 \):
\[ 252 \times 594 = 149688 \]

4. **Set Up the Equation**:
Now we can set up the equation:
\[ 8316 \times \text{HCF}(252, 594) = 149688 \]

5. **Solve for HCF**:
To find HCF, we rearrange the equation:
\[ \text{HCF}(252, 594) = \frac{149688}{8316} \]

6. **Perform the Division**:
Now we perform the division:
\[ \text{HCF}(252, 594) = 18 \]

### Final Answer:
Thus, the HCF of 252 and 594 is **18**.