HCF of three numbers A, B and C is 13. LCM of B and C is 910 and LCM of A and B is 195. If the number B is 65. Find the other numbers A and C.
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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.