If HCF (209, 737) = 11 and LCM (209, 737) = 209 x, then the value of x is :

Options

A. 67
B. 72
C. 77
D. 81

Answer

To find the value of \( x \) in the equation \( \text{LCM}(209, 737) = 209 \times x \), given that \( \text{HCF}(209, 737) = 11 \), we can use the relationship between HCF, LCM, and the product of two numbers.

### Step-by-step Solution:

1. **Recall the relationship between HCF, LCM, and the product of two numbers**:
\[ \text{HCF}(a, b) \times \text{LCM}(a, b) = a \times b \]
Here, \( a = 209 \) and \( b = 737 \).

2. **Substitute the known values into the equation**:
\[ 11 \times (209 \times x) = 209 \times 737 \]

3. **Simplify the equation**:
\[ 11 \times 209 \times x = 209 \times 737 \]

4. **Divide both sides by \( 209 \)** (since \( 209 \) is not zero):
\[ 11 \times x = 737 \]

5. **Now, solve for \( x \)**:
\[ x = \frac{737}{11} \]

6. **Calculate the value**:
\[ x = 67 \]

Thus, the value of \( x \) is \( 67 \).