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. This question is definitely too tough for CAT, but is a wonderful question to conquer that fear of the unknown (x). A range of CAT questions can be asked based on the concept of HCF and LCM. HCF and 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.

Question 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").


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Explanatory Answer

Method of solving this CAT Question from Number Theory - HCF and LCM: It is vital not to be intimidated by questions that have a lot of variables in them.

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.

The question is "Find LCM of a, b, c."

Hence the answer is "Cannot be determined"

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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