If A and B are positive integers such that the least common multiple

Question

If A and B are positive integers such that the least common multiple of A and B is 72 ,what is the remainder when the product AB is divided by 8?

A. 0

B. 1

C. 2

D. 3

E. 4

Sapnilbhatnagar · Answer

Since A and B are both factors of 72 they will both be divisible by 8. Since A and B are divisible by 8 their product will be divisible by 8.
IMO A.

stne · Answer

72= 2*2*2*3*3

Among many combinations for A and B lets take A=8 and B=9 
A*B= 72 So 72 divided by 8 gives remainder 0

Ans = A

( Other values that A and B could take: A= 4 B=72, A=18 B=8, etc. in all cases remainder when A*B is divided by 8 is zero)

Hope it's clear.

stne · Answer

Hi  Sapnilbhatnagar ,
Your solution is correct, but just a note, both A and B need not be divisible by 8, e.g. a= 9 b=8 or a=18, b=8 , etc one of them has to be divisible by 8 and one has to be divisible by 9 for their LCM to be 72.

Hope it helps.

bumpbot · Answer

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If A and B are positive integers such that the least common multiple

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