The LCM and HCF of 2 numbers are 168 and 6 respectively. If one of the numbers is 24. find the other.
A. 36
B. 38
C. 40
D. 42

Options

A. D
B. B
C. A
D. C

Answer

To find the other number when given the LCM, HCF, and one of the numbers, we can use the relationship between these values.

### Step-by-step Solution:

1. **Understand the relationship between LCM, HCF, and the two numbers:**
The relationship is given by the formula:
\[ \text{LCM} \times \text{HCF} = \text{Number 1} \times \text{Number 2} \]
Here, we know:
- LCM = 168
- HCF = 6
- Number 1 = 24
- Number 2 = x (the unknown we need to find)

2. **Substitute the known values into the formula:**
\[ 168 \times 6 = 24 \times x \]

3. **Calculate the left-hand side:**
\[ 168 \times 6 = 1008 \]
So, we have:
\[ 1008 = 24 \times x \]

4. **Solve for x:**
To find x, divide both sides of the equation by 24:
\[ x = \frac{1008}{24} \]

5. **Perform the division:**
\[ x = 42 \]

6. **Conclusion:**
The other number is 42.

### Final Answer:
The other number is **42** (Option D).