The HCF of two numbers 24 and their LCM is 216. If one of the number is 72, then the other number is

Options

A. 27
B. 72
C. 8
D. 24

Answer

To solve the problem, we need to find the other number when one number is given as 72, the HCF is 24, and the LCM is 216. We can use the relationship between HCF, LCM, and the two numbers.

### Step-by-Step Solution:

1. **Understand the relationship**: The relationship between two numbers (let's call them \( a \) and \( b \)), their HCF (Highest Common Factor), and their LCM (Lowest Common Multiple) is given by the formula:
\[ a \times b = \text{HCF} \times \text{LCM} \]

2. **Assign values**: From the problem, we know:
- One number \( a = 72 \)
- HCF = 24
- LCM = 216
- Let the other number be \( b \).

3. **Substitute into the formula**: Plugging the known values into the formula gives us:
\[ 72 \times b = 24 \times 216 \]

4. **Calculate the right-hand side**: First, calculate \( 24 \times 216 \):
\[ 24 \times 216 = 5184 \]

5. **Set up the equation**: Now we have:
\[ 72 \times b = 5184 \]

6. **Solve for \( b \)**: To find \( b \), divide both sides by 72:
\[ b = \frac{5184}{72} \]

7. **Perform the division**: Calculate \( \frac{5184}{72} \):
\[ b = 72 \]

8. **Conclusion**: Therefore, the other number is \( 72 \).

### Final Answer:
The other number is \( 72 \).