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

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Bunuel
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If 72^4 is the greatest common divisor of positive integers A and B, a [#permalink] New post   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
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garyster
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Re: If 72^4 is the greatest common divisor of positive integers A and B, a [#permalink] New post   18 Oct 2018, 02:38
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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

Answer is B

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If 72^4 is the greatest common divisor of positive integers A and B, a [#permalink] New post   18 Oct 2018, 02:39
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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
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Re: If 72^4 is the greatest common divisor of positive integers A and B, a [#permalink] New post   18 Oct 2018, 03:33
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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
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If 72^4 is the greatest common divisor of positive integers A and B, a [#permalink] New post   24 Oct 2018, 00:03
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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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Re: If 72^4 is the greatest common divisor of positive integers A and B, a [#permalink] New post   05 Dec 2019, 00:02
LCM(x,y)*GCF(x,y) = X*Y
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Re: If 72^4 is the greatest common divisor of positive integers A and B, a [#permalink] New post   05 Dec 2019, 01:41
We know that:
Product of two Numbers= LCM*HCF

AB= 72^4 * 72^6 = 72^10

Answer: B
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Re: If 72^4 is the greatest common divisor of positive integers A and B, a [#permalink] New post   05 Dec 2019, 02:29
The two concepts that are used in solving this question are:

1) \(X^m\) * \(X^n\) = \(X^{m+n}\) and

2) HCF x LCM = Product of 2 numbers

The question says that the HCF of the two numbers is \(72^4\) and the LCM of the same numbers is \(72^6\). Using the second concept stated above, we can say,
A x B = \(72^4 * 72^6\).

Using the first concept stated above, the RHS of this equation can be rewritten as \(72^{10}\). Therefore, we can conclude that AB =\( 72^{10}\). The correct answer option is B.

Hope that helps!
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Re: If 72^4 is the greatest common divisor of positive integers A and B, a [#permalink] New post   05 Oct 2023, 13:28
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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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