The HCF of two numbers is 11 and their LCM is 330 .If one of the number is 55. Find the other number .

Options

A. 33
B. 66
C. 44
D. 77

Answer

To find the other number when the HCF (Highest Common Factor) is 11, the LCM (Least Common Multiple) is 330, and one of the numbers is 55, we can use the relationship between HCF, LCM, and the two numbers.

### Step-by-Step Solution:

1. **Understand the Relationship**:
The relationship between two numbers \( a \) and \( b \) with their HCF and LCM is given by:
\[ \text{HCF} \times \text{LCM} = a \times b \]
Here, we know:
- HCF = 11
- LCM = 330
- One number \( a = 55 \)

2. **Set Up the Equation**:
Substitute the known values into the equation:
\[ 11 \times 330 = 55 \times b \]

3. **Calculate the Left Side**:
Calculate \( 11 \times 330 \):
\[ 11 \times 330 = 3630 \]

4. **Set Up the Equation for \( b \)**:
Now we have:
\[ 3630 = 55 \times b \]

5. **Solve for \( b \)**:
To find \( b \), divide both sides by 55:
\[ b = \frac{3630}{55} \]

6. **Perform the Division**:
Calculate \( \frac{3630}{55} \):
\[ b = 66 \]

7. **Conclusion**:
The other number is \( 66 \).

### Final Answer:
The other number is **66**.

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