Question

Two numbers are in the ratio 8 : 11 and their LCM is 2816. What would be the difference between the two numbers?

• A. 64
• B. 72
• C. 84
• D. 96
• E. 256

Answer 1

The Correct Option is D

Step 1: Understand the problem.
We are given that two numbers are in the ratio 8 : 11 and their LCM is 2816. We are asked to find the difference between the two numbers.

Step 2: Let the two numbers be \( 8x \) and \( 11x \).
Since the two numbers are in the ratio 8 : 11, we can express the two numbers as \( 8x \) and \( 11x \), where \( x \) is a common factor.

Step 3: Use the relationship between LCM and GCD.
The formula relating LCM, GCD, and the product of two numbers is:
\( \text{LCM}(a, b) \times \text{GCD}(a, b) = a \times b \)
For the numbers \( 8x \) and \( 11x \), the GCD is \( x \) (since 8 and 11 are coprime). Therefore, we have:
\( \text{LCM}(8x, 11x) = \frac{8x \times 11x}{x} = 88x \)
We are given that the LCM is 2816, so:
\( 88x = 2816 \)
Solving for \( x \):
\( x = \frac{2816}{88} = 32 \)

Step 4: Calculate the two numbers.
The two numbers are:
- First number: \( 8x = 8 \times 32 = 256 \)
- Second number: \( 11x = 11 \times 32 = 352 \)

Step 5: Find the difference between the two numbers.
The difference between the two numbers is:
\( 352 - 256 = 96 \)

Step 6: Conclusion.
The difference between the two numbers is 96.

Final Answer:
The correct answer is (D): 96.