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

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

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New post 11 Feb 2019, 18:18
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Question Stats:

67% (01:35) correct 33% (01:32) wrong based on 24 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
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Posts: 59
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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New post 11 Feb 2019, 20:47
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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]

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New post 16 Feb 2019, 19:52
Official Answer

4 and 5 are relative prime numbers
A=4G
B=5G

L=4·5·G=160
20G=160, G=8
A
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Concentration: Strategy, Marketing
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Re: If the least common multiple of positive integers A and B is 160 and A  [#permalink]

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New post 17 Feb 2019, 22:24
philipssonicare wrote:
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


Since LCM is 160, both numbers A & B together must have all the roots of 160.

Roots of 160 are = 5*2*2*2*2*2 = 5 * (2^5)

Now since A/B = 4/5 = (2^2)/5
=> A has 2^2 as additional factors over B
and B has 5 as additional factor A
(2^3) are the remaining roots between A and B which must b common.

=> A can be equal to 2^5
and B can be equal to (2^3)*5

Hence the GCD between the two is (2^3) = 8

Therefore option A is the correct answer.
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Re: If the least common multiple of positive integers A and B is 160 and A   [#permalink] 17 Feb 2019, 22:24
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If the least common multiple of positive integers A and B is 160 and A

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