The HCF and LCM of the two numbers is 12 and 600 respectively . If one of the numbers is 48, then the other number will be

Options

A. 150
B. 400
C. 1500
D. none of these

Answer

To find the other number when one number is given, we can use the relationship between the HCF (Highest Common Factor), LCM (Lowest Common Multiple), and the two numbers. Here’s how to solve the problem step by step:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- HCF (n1, n2) = 12
- LCM (n1, n2) = 600
- One number (n1) = 48
- We need to find the other number (n2).

2. **Use the Relationship Between HCF, LCM, and the Two Numbers:**
The relationship states that:
\[ \text{HCF} \times \text{LCM} = n1 \times n2 \]
Substituting the known values:
\[ 12 \times 600 = 48 \times n2 \]

3. **Calculate the Left Side:**
\[ 12 \times 600 = 7200 \]
So we have:
\[ 7200 = 48 \times n2 \]

4. **Solve for n2:**
To find n2, divide both sides by 48:
\[ n2 = \frac{7200}{48} \]

5. **Perform the Division:**
\[ n2 = 150 \]

6. **Conclusion:**
The other number is 150.

### Final Answer:
The other number is **150**.