The LCM of two numbers is 520 and their HCF is 4. If one of the numbers is 52, then the other number is:

Options

A. 40
B. 42
C. 50
D. 52

Answer

To find the other number when the LCM of two numbers is 520, their HCF is 4, and one of the numbers is 52, we can use the relationship between LCM, HCF, and the two numbers.

### Step-by-Step Solution:

1. **Understand the Relationship**:
The relationship between the two numbers (let's call them \( n_1 \) and \( n_2 \)), their LCM, and HCF is given by the formula:
\[ \text{LCM}(n_1, n_2) \times \text{HCF}(n_1, n_2) = n_1 \times n_2 \]

2. **Assign Values**:
We know:
- \( \text{LCM} = 520 \)
- \( \text{HCF} = 4 \)
- One of the numbers \( n_1 = 52 \)
- The other number \( n_2 = x \) (which we need to find)

3. **Plug in the Values**:
Substitute the known values into the formula:
\[ 520 \times 4 = 52 \times x \]

4. **Calculate the Left Side**:
Calculate \( 520 \times 4 \):
\[ 520 \times 4 = 2080 \]

5. **Set Up the Equation**:
Now we have:
\[ 2080 = 52 \times x \]

6. **Solve for \( x \)**:
To find \( x \), divide both sides by 52:
\[ x = \frac{2080}{52} \]

7. **Calculate \( x \)**:
Perform the division:
\[ x = 40 \]

8. **Conclusion**:
The other number is \( 40 \).

### Final Answer:
The other number is **40**.