The HCF and LCM of two numbers are 12 and 240 respectively. If the firstnumbers is 24, what is the second numbers ?

Options

A. 144
B. 288
C. 264
D. 120

Answer

To find the second number when the HCF and LCM of two numbers are given, we can use the relationship between HCF, LCM, and the two numbers. The formula we will use is:

\[ \text{HCF} \times \text{LCM} = \text{First Number} \times \text{Second Number} \]

### Step-by-Step Solution:

1. **Identify the Given Values:**
- HCF = 12
- LCM = 240
- First Number = 24

2. **Substitute the Values into the Formula:**
\[ 12 \times 240 = 24 \times \text{Second Number} \]

3. **Calculate the Left Side:**
\[ 12 \times 240 = 2880 \]

4. **Set Up the Equation:**
\[ 2880 = 24 \times \text{Second Number} \]

5. **Solve for the Second Number:**
- Divide both sides by 24:
\[ \text{Second Number} = \frac{2880}{24} \]

6. **Calculate the Division:**
\[ \text{Second Number} = 120 \]

### Final Answer:
The second number is **120**.