If 72^4 is the greatest common divisor of positive integers A and B, a : Problem Solving (PS)

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

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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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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

Spoiler: OA

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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, 02:38

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

Answer is B

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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

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

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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

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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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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