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# If 72^4 is the greatest common divisor of positive integers A and B, a

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Math Expert
Joined: 02 Sep 2009
Posts: 58410
If 72^4 is the greatest common divisor of positive integers A and B, a  [#permalink]

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18 Oct 2018, 02:31
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Difficulty:

35% (medium)

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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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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18 Oct 2018, 02:38
1
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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Joined: 13 Mar 2018
Posts: 23
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WE: Project Management (Other)
If 72^4 is the greatest common divisor of positive integers A and B, a  [#permalink]

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18 Oct 2018, 02:39
1
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
Joined: 08 Oct 2018
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Re: If 72^4 is the greatest common divisor of positive integers A and B, a  [#permalink]

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18 Oct 2018, 03:33
3
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
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Joined: 13 Jan 2018
Posts: 342
Location: India
Concentration: Operations, General Management
GMAT 1: 580 Q47 V23
GMAT 2: 640 Q49 V27
GPA: 4
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If 72^4 is the greatest common divisor of positive integers A and B, a  [#permalink]

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24 Oct 2018, 00:03
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 72^4 is the greatest common divisor of positive integers A and B, a   [#permalink] 24 Oct 2018, 00:03
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