CAT Practice : Number System - HCF, LCM

You are here: Home  CAT Questionbank   CAT Quant  Number System: HCF, LCM  Question 3
It is vital not to be intimidated by questions that have a lot of variables in them. This question is definitely too tough for CAT, but is a wonderful question to conquer that fear of the unknown (x).

HCF LCM - Theory

    Q.3: There are three numbers a,b, c such that HCF (a, b) = l, HCF (b, c) = m and HCF (c, a) = n. HCF (l, m) = HCF (l, n) = HCF (n, m) = 1. Find LCM of a, b, c. (The answer can be "This cannot be determined").


  • Correct Answer
    Cannot be determined

Detailed Solution

a is a multiple of l and n. Also HCF (l,n) =1; => a has to be a multiple of ln, similarly b has to be a multiple of lm and c has to be a multiple of mn.

We can assume, a = lnx, b = lmy, c = mnz.
Now given that HCF(a, b) = l, that means HCF(nx, my) = 1. This implies HCF(x, y) = 1 and HCF(m, x) = HCF(n, y) = 1.

Similarly it can also be shown that HCF(y, z) = HCF(z, x) = 1 and others also.
So in general it can be written any two of the set {l, m, n, x, y, z} are co-prime.
Now LCM(a, b, c) = LCM (lnx, lmy, mnz) = lmnxyz = abc/lmn.

Quiet obviously, it is a reasonable assumption that a question in CAT will not be as tough as the last one here. However, it is a good question to get an idea of the properties of LCM and HCF.

Correct Answer: Cannot be determined

Our Online Course, Now on Google Playstore!

2IIM's App

Fully Functional Course on Mobile

All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.

Cache Content for Offline Viewing

Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!

Get it on Google Play

More questions from Number Theory - HCF, LCM

  1. HCF LCM
  2. Remainders LCM
  3. HCF LCM - Theory
  4. HCF basics
  5. HCF LCM
  6. HCF basics
  7. HCF basics
Number Theory is one of the most heavily tested topics. Within this, one should get the basics on factors, multiples, HCF, LCM very clear before moving on to the tougher sets.