if d and m are the GCD and LCM of two positive integers a, b respectively, then prove that dm=ab.
Answer (1)
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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