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if d and m are the GCD and LCM of two positive integers a, b respectively, then prove that dm=ab.


Bigray Dzienny 26th Nov, 2019
Answer (1)
Avishek Dutta 28th Nov, 2019

A=set containing prime factors of a where repitition is allowed in a set is assumed

B=set containing prime factors of b where repitition is allowed in a set is assumed

m=product of the elements of (A union B)

d=product of the elements of (A intersection B)

dm=product of the elements of (A union B) and (A intersection B)

=Product of the elements of A-B ,B-A,(A intersection B),(A intersection B)

=product of the elements of A and B

=ab(proved)


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