The HCF and LCM of two natural numbers are 12 and 72 ,respectively.What is the difference between the two numbers, if one of the number is 24?

Options

A. 12
B. 18
C. 21
D. 24

Answer

To find the difference between the two numbers given that the HCF is 12, the LCM is 72, and one of the numbers is 24, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between HCF, LCM, and the two numbers**:
The relationship between the HCF (Highest Common Factor), LCM (Lowest Common Multiple), and the two numbers can be expressed as:
\[ \text{HCF} \times \text{LCM} = \text{Number 1} \times \text{Number 2} \]
Here, we know:
- HCF = 12
- LCM = 72
- Number 1 = 24 (given)

2. **Substitute the known values into the formula**:
Plugging in the values we have:
\[ 12 \times 72 = 24 \times \text{Number 2} \]

3. **Calculate the left side**:
Now, calculate \(12 \times 72\):
\[ 12 \times 72 = 864 \]

4. **Set up the equation**:
Now we have:
\[ 864 = 24 \times \text{Number 2} \]

5. **Solve for Number 2**:
To find Number 2, divide both sides by 24:
\[ \text{Number 2} = \frac{864}{24} \]

6. **Calculate Number 2**:
Now perform the division:
\[ \text{Number 2} = 36 \]

7. **Find the difference between the two numbers**:
Now that we have both numbers (24 and 36), we can find the difference:
\[ \text{Difference} = |36 - 24| = 12 \]

### Final Answer:
The difference between the two numbers is **12**.

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