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Prove-by-set-theory-or-otherwise-lcm-gcd-x-y-gcd-y-z-gcd-z-x-is-equal-to-gcd-lcm-x-y-lcm-y-z-lcm-z-x-Or-give-a-counter-example-

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Question Number 94955 by Rasheed.Sindhi last updated on 22/May/20
Prove by set theory or otherwise lcm( gcd(x,y),gcd(y,z),gcd(z,x) ) is equal to gcd( lcm(x,y),lcm(y,z),lcm(z,x) ) Or give a counter example.
Provebysettheoryorotherwiselcm(gcd(x,y),gcd(y,z),gcd(z,x))isequaltogcd(lcm(x,y),lcm(y,z),lcm(z,x))Orgiveacounterexample.

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