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Math Expert V
Joined: 02 Sep 2009
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If 72^4 is the greatest common divisor of positive integers A and B, a  [#permalink]

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Question Stats: 69% (00:59) correct 31% (01:34) wrong based on 120 sessions

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If 72^4 is the greatest common divisor of positive integers A and B, and 72^6 is the least common multiple of A and B, then AB =

A. 72^6
B. 72^10
C. 72^12
D. 72^24
E. 72^4096

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Intern  B
Joined: 29 Jan 2017
Posts: 6
Re: If 72^4 is the greatest common divisor of positive integers A and B, a  [#permalink]

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Product of any two numbers is always equal to product of their LCM and HCF
So, A*B= 72^4 * 72^6= 72^10

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Intern  B
Joined: 13 Mar 2018
Posts: 23
GPA: 3.12
WE: Project Management (Other)
If 72^4 is the greatest common divisor of positive integers A and B, a  [#permalink]

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Bunuel wrote:
If 72^4 is the greatest common divisor of positive integers A and B, and 72^6 is the least common multiple of A and B, then AB =

A. 72^6
B. 72^10
C. 72^12
D. 72^24
E. 72^4096

we know that:
if HCF of A & B is H and
if LCM of A & B is L

then H*L= A*B -----> Product of HCF and LCM of two numbers is equal to product of two numbers

Then therefore, from the question, A*B= $$72^4$$ * $$72^6$$ = $$72^{10}$$, Hence correct option is B
Intern  B
Joined: 08 Oct 2018
Posts: 7
Re: If 72^4 is the greatest common divisor of positive integers A and B, a  [#permalink]

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Bunuel wrote:
If 72^4 is the greatest common divisor of positive integers A and B, and 72^6 is the least common multiple of A and B, then AB =

A. 72^6
B. 72^10
C. 72^12
D. 72^24
E. 72^4096

since 72^4 is the GCF and 72^6 the the LCM of A,B.Hence AB is GCF*LCM=72^10
HENCE B is the correct answer
Senior Manager  P
Joined: 13 Jan 2018
Posts: 342
Location: India
Concentration: Operations, General Management
GMAT 1: 580 Q47 V23 GMAT 2: 640 Q49 V27 GPA: 4
WE: Consulting (Consulting)
If 72^4 is the greatest common divisor of positive integers A and B, a  [#permalink]

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A and B have GCD $$72^4$$.

So $$72^4$$ must be common in both A and B.

Now A and B have LCM $$72^6$$. As $$72^4$$ is already common in A and B, either of these numbers should take $$72^6$$

A = $$72^4$$ , B = $$72^6$$

Or

A = $$72^6$$ , B = $$72^4$$

PS: Remember, no other case is possible apart from these two.

So AB = $$72^6$$ * $$72^4$$

AB = $$72^{10}$$

OPTION : B
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Chaitanya

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if you like my explanation!!! If 72^4 is the greatest common divisor of positive integers A and B, a   [#permalink] 24 Oct 2018, 00:03
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