The HCF and the LCM of two numbers are 24 and 1008. If one of the numbers is 168, then find the other number

Options

A. 336
B. 252
C. 148
D. 144

Answer

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

\[ \text{HCF} \times \text{LCM} = \text{Number 1} \times \text{Number 2} \]

Let's denote:
- HCF = 24
- LCM = 1008
- Number 1 = 168
- Number 2 = x (the number we need to find)

### Step-by-Step Solution:

1. **Write the formula**:
\[ \text{HCF} \times \text{LCM} = \text{Number 1} \times \text{Number 2} \]
Substituting the known values:
\[ 24 \times 1008 = 168 \times x \]

2. **Calculate the left side**:
\[ 24 \times 1008 = 24192 \]
So, we have:
\[ 24192 = 168 \times x \]

3. **Rearrange the equation to solve for x**:
\[ x = \frac{24192}{168} \]

4. **Perform the division**:
To simplify \( \frac{24192}{168} \):
- First, simplify by dividing both the numerator and the denominator by 24:
\[ \frac{24192 \div 24}{168 \div 24} = \frac{1008}{7} \]

5. **Calculate \( \frac{1008}{7} \)**:
- Performing the division:
\[ 1008 \div 7 = 144 \]

6. **Conclusion**:
Therefore, the other number is:
\[ x = 144 \]

### Final Answer:
The other number is **144**.