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Find the missing number from HCF and LCM: Two numbers have HCF = 15 and LCM = 225. If one number is 75, find the other number.

Difficulty: Easy

Correct Answer: 45

Explanation:


Introduction / Context:
For two numbers m and n, the identity m * n = HCF(m, n) * LCM(m, n) lets us find the unknown when one number and both HCF and LCM are known. This avoids trial-and-error completely.


Given Data / Assumptions:

  • HCF = 15
  • LCM = 225
  • One number = 75


Concept / Approach:
Compute the product of HCF and LCM to get m * n, then divide by the known number to obtain the unknown partner. Ensure the quotient is an integer to validate consistency.


Step-by-Step Solution:

m * n = 15 * 225 = 3375.Given one number is 75, the other is 3375 / 75 = 45.


Verification / Alternative check:

Check HCF(75, 45) = 15 and LCM(75, 45) = 225; their product is 3375, matching the identity.


Why Other Options Are Wrong:

  • 105, 90, 60 do not jointly yield HCF 15 and LCM 225 with 75 under the product identity.


Common Pitfalls:

  • Forgetting the product identity or miscalculating 3375/75.


Final Answer:

45
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