The ratio of two numbers is 9 : 11 and their HCF is 18, then their LCM is:

Options

A. 1718
B. 1782
C. 1582
D. 1208

Answer

To find the LCM of two numbers given their ratio and HCF, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ratio and HCF**:
- The ratio of the two numbers is given as 9:11.
- The HCF (Highest Common Factor) of the two numbers is given as 18.

2. **Express the Numbers in Terms of HCF**:
- Let the two numbers be represented as:
- First number = HCF × 9k = 18 × 9k = 162k
- Second number = HCF × 11k = 18 × 11k = 198k
- Here, k is a common multiplier that we will use to express the numbers.

3. **Calculate the Actual Numbers**:
- Since HCF is 18, we can find the actual numbers:
- First number = 18 × 9 = 162
- Second number = 18 × 11 = 198

4. **Use the Formula for LCM**:
- The relationship between HCF, LCM, and the product of the two numbers is given by:
\[ \text{LCM} \times \text{HCF} = \text{Product of the two numbers} \]
- Therefore, we can rearrange this to find LCM:
\[ \text{LCM} = \frac{\text{Product of the two numbers}}{\text{HCF}} \]

5. **Calculate the Product of the Two Numbers**:
- Calculate the product of the two numbers:
\[ 162 \times 198 \]

6. **Calculate the LCM**:
- Substitute the values into the LCM formula:
\[ \text{LCM} = \frac{162 \times 198}{18} \]

7. **Perform the Calculation**:
- First, calculate \(162 \times 198 = 32136\).
- Then divide by HCF (18):
\[ \text{LCM} = \frac{32136}{18} = 1782 \]

### Final Answer:
The LCM of the two numbers is **1782**.

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