Given that HCF ( 252, 594) = 18 find LCM ( 252 , 594)

Options

A. `8316`
B. `9316`
C. `4421`
D. `6314`

Explanation

To find the LCM (Least Common Multiple) of the numbers 252 and 594 given that their HCF (Highest Common Factor) is 18, we can use the relationship between HCF and LCM. The formula is:

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

### Step-by-step Solution:

1. **Identify the Given Values:**
- HCF (252, 594) = 18
- The two numbers are 252 and 594.

2. **Calculate the Product of the Two Numbers:**
\[ \text{Product} = 252 \times 594 \]

3. **Perform the Multiplication:**
\[ 252 \times 594 = 149688 \]

4. **Use the HCF to Find the LCM:**
We can rearrange the formula to find the LCM:
\[ \text{LCM} = \frac{\text{Product of the two numbers}}{\text{HCF}} \]
Substituting the values we have:
\[ \text{LCM} = \frac{149688}{18} \]

5. **Perform the Division:**
\[ \text{LCM} = 8316 \]

### Final Answer:
The LCM of 252 and 594 is **8316**.