CAT Quantitative Aptitude Questions | CAT Number Systems - HCF and LCM questions

CAT Questions | Number Theory | HCF and LCM

The question is about HCF and LCM. When we know the LCM of two numbers, how do we find out the LCM of another related pair of numbers. A range of CAT questions can be asked based on this simple concept. HCF-LCM from CAT Number Systems is oft tested not just in the context of CAT Number Systems but also inside CAT Quantitative Aptitude questions from other topics. 2IIM has provided fabulous questions with detailed solution for the topic of HCF-LCM in the Free CAT Question bank.

Question 8: There are 2 numbers such that a > b, HCF (a, b) = h and LCM (a, b) = l. What is the LCM of a – b and b?

  1. l
  2. (a - b) b
  3. (a - b) b / h
  4. h (a - b)

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Explanatory Answer

Method of solving this CAT Question from Number Theory - HCF and LCM: Product of 2 numbers = LCM * HCF.

Given a > b, HCF = h, LCM = l
From the above we can say, HCF of (a – b, b) = h

LCM x HCF = Product of 2 numbers
(a – b)b = h x LCM
LCM = (a - b) b / h

The question is "What is the LCM of a – b and b?"

Hence the answer is "(a - b) b / h"

Choice C is the correct answer.


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