The HCF and LCM of the two numbers is 12 and 600 respectively . If one of the number is 24, then the other number will be

Options

A. 300
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 = 12
- LCM = 600
- One number (let's call it A) = 24
- Let the other number be B (which we need to find).

2. **Use the relationship between HCF, LCM, and the two numbers**:
- The relationship is given by the formula:
\[ \text{HCF} \times \text{LCM} = A \times B \]
- Substituting the known values into the formula:
\[ 12 \times 600 = 24 \times B \]

3. **Calculate the left side**:
- First, calculate \(12 \times 600\):
\[ 12 \times 600 = 7200 \]

4. **Set up the equation**:
- Now we have:
\[ 7200 = 24 \times B \]

5. **Solve for B**:
- To find B, divide both sides by 24:
\[ B = \frac{7200}{24} \]

6. **Perform the division**:
- Calculate \(7200 \div 24\):
\[ 7200 \div 24 = 300 \]

7. **Conclusion**:
- Therefore, the other number (B) is 300.

### Final Answer:
The other number is **300**.

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