The HCF and LCM of two numbers are 24 and 5304 respectively. If first number is 408, then first number exceeds the 2nd number by

Options

A. 88
B. 96
C. 102
D. 312

Answer

To solve the problem step by step, we will use the relationship between the HCF (Highest Common Factor), LCM (Lowest Common Multiple), and the two numbers involved.

### Step-by-Step Solution:

1. **Given Information**:
- HCF (Highest Common Factor) = 24
- LCM (Lowest Common Multiple) = 5304
- First number (let's call it A) = 408
- Second number (let's call it B) = ?

2. **Using the Relationship**:
We know that:
\[ \text{HCF} \times \text{LCM} = A \times B \]
Plugging in the values we have:
\[ 24 \times 5304 = 408 \times B \]

3. **Calculating the Left Side**:
First, we calculate \( 24 \times 5304 \):
\[ 24 \times 5304 = 127296 \]

4. **Setting Up the Equation**:
Now we have:
\[ 127296 = 408 \times B \]

5. **Solving for B**:
To find B, we rearrange the equation:
\[ B = \frac{127296}{408} \]
Now we perform the division:
\[ B = 312 \]

6. **Finding the Difference**:
Now we need to find how much the first number exceeds the second number:
\[ \text{Difference} = A - B = 408 - 312 \]
Calculating the difference:
\[ \text{Difference} = 96 \]

### Final Answer:
The first number exceeds the second number by **96**.

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