The LCM of two numbers is 520 and their HCF s 4. If one of the number 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 and HCF of two numbers are given, we can use the relationship between them. Here's how to solve the problem step by step:

### Step-by-Step Solution:

1. **Understand the relationship**: The relationship between the LCM (Least Common Multiple), HCF (Highest Common Factor), and the two numbers can be expressed as:
\[ \text{LCM} \times \text{HCF} = \text{First Number} \times \text{Second Number} \]

2. **Identify the known values**: From the problem, we know:
- LCM = 520
- HCF = 4
- First Number = 52
- Second Number = ?

3. **Substitute the known values into the formula**:
\[ 520 \times 4 = 52 \times \text{Second Number} \]

4. **Calculate the left side**:
\[ 520 \times 4 = 2080 \]
So, we have:
\[ 2080 = 52 \times \text{Second Number} \]

5. **Solve for the Second Number**:
To find the Second Number, divide both sides by 52:
\[ \text{Second Number} = \frac{2080}{52} \]

6. **Perform the division**:
\[ \text{Second Number} = 40 \]

### Conclusion:
The other number is **40**.

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