Two natural numbers have HCF 12 and LCM 72. If one number is 24, what is the difference between the two numbers?
Aptitude
Problems on H.C.F and L.C.M
Difficulty: Easy
Choose an option
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A12
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B18
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C21
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D24
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E6
Answer
Correct Answer: 12
Explanation
Introduction: The product of two numbers equals the product of their HCF and LCM. Knowing one number allows us to find the other directly, then compute the difference.
Given Data / Assumptions:
- HCF = 12
- LCM = 72
- One number = 24
Concept / Approach: a * b = HCF * LCM. Solve for the unknown and subtract to find the difference.
Step-by-Step Solution:
a * b = 12 * 72 = 864 If a = 24, then b = 864 / 24 = 36 Difference = 36 - 24 = 12Verification / Alternative check: HCF(24, 36) = 12 and LCM(24, 36) = 72, confirming consistency.
Why Other Options Are Wrong: 18, 21, and 24 do not match the computed difference for the consistent pair.
Common Pitfalls: Using sum instead of product relation, or forgetting to check that the derived pair satisfies both HCF and LCM values.
Final Answer: 12