GCD and LCM relation

greatest-common-divisor lcm
Abidi picture Abidi · Apr 10, 2011 · Viewed 15.2k times · Source

The following relation works only for two (3, 12) numbers, it fails to produce the right answer when used for three numbers (3,12,10) . Just wondering if is it my understanding or it is just for two numbers and for me same is true for Euclid algorithm as well.

LCM(a, b) = (a x b) / GCD(a,b) or GCD(a,b) = (a x b) / LCM(a, b)

Answer

Don Roby picture Don Roby · Apr 10, 2011

The analogous formulas to

LCM(a, b) = (a x b) / GCD(a,b) or GCD(a,b) = (a x b) / LCM(a, b)

with three variables are simply not valid, as your example with (3, 12, 10) shows readily.

The product of these three numbers is 360. The GCD is 1. The LCM is 60.

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