# CAT Practice : Number System - HCF, LCM

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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").

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.

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## More questions from Number Theory - HCF, LCM

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.