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# If the least common multiple of positive integers A and B is 160 and A

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Manager
Joined: 15 Feb 2018
Posts: 242
If the least common multiple of positive integers A and B is 160 and A  [#permalink]

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11 Feb 2019, 18:18
00:00

Difficulty:

35% (medium)

Question Stats:

67% (01:33) correct 33% (01:10) wrong based on 6 sessions

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If the least common multiple of positive integers A and B is 160 and A:B=4:5, what is the greatest common divisor of A and B?

A) 8
B) 9
C) 10
D) 12
E) 15
Manager
Joined: 07 Aug 2017
Posts: 60
Location: India
GPA: 4
WE: Information Technology (Consulting)
Re: If the least common multiple of positive integers A and B is 160 and A  [#permalink]

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11 Feb 2019, 20:47
From the ratio we can consider A=4x and B=5x.
GCD(A,B)=x

Property of LCM, GCD says, $$A*B=LCM(A,B)*GCD(A,B)$$
$$20x^2=160*x$$
$$20x=160$$
$$x=8$$
GCD(A,B)=8

Ans - A

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Re: If the least common multiple of positive integers A and B is 160 and A   [#permalink] 11 Feb 2019, 20:47
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