The HCF of two numbers is 15 and their LCM is 300. If one of the numbers is 60, the other is :

Options

A. 50
B. 75
C. 65
D. 100

Answer

To find the other number when given the HCF (Highest Common Factor), LCM (Lowest Common Multiple), and one of the numbers, we can use the relationship between these values.

### Step-by-Step Solution:

1. **Understand the relationship**: The relationship between the HCF, LCM, and the two numbers can be expressed as:
\[ \text{HCF} \times \text{LCM} = \text{Number 1} \times \text{Number 2} \]
In this case, we know:
- HCF = 15
- LCM = 300
- Number 1 = 60
- Number 2 = n (the unknown number we want to find)

2. **Set up the equation**: Substitute the known values into the equation:
\[ 15 \times 300 = 60 \times n \]

3. **Calculate the left side**: Calculate \(15 \times 300\):
\[ 15 \times 300 = 4500 \]

4. **Set up the equation**: Now we have:
\[ 4500 = 60 \times n \]

5. **Solve for n**: To find n, divide both sides by 60:
\[ n = \frac{4500}{60} \]

6. **Calculate the division**: Perform the division:
\[ n = 75 \]

7. **Conclusion**: The other number is 75.

### Final Answer:
The other number is **75**.