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The most important property of LCM (the least common multiple) and GCD (the greatest common divisors) is: for any positive integers \(x\) and \(y\), \(x*y=GCD(x,y)*LCM(x,y)\), so AB=72*6=432.

Re: If the LCM of A and B is 72 and their HCF is 6, what is the [#permalink]

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15 Feb 2013, 09:49

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Expert's post

Try to understand why is so.

take two numbers a and b

The prime factorization of those numbers is

a= d,d,e,r b=d,e,g,h,i

HCF of a and b = d,e LCM of a and b = d,e,d,r,g,h,i Product of HCF and LCM = d.e.d.e.d.r.g.h.i ---------> d^3.e^2.r.g.h.i Product of Numbers = d.d.e.r.d.e.g.h.i --------------> d^3.e^2.r.g.h.i

in my opinion it is better to understand any theorem/rule than to remember it.

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