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

Question

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

garyster · Accepted Answer

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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AnupamKT · Answer

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

DEEPIKA29 · Answer

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

eswarchethu135 · Answer

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

dcummins · Answer

LCM(x,y)*GCF(x,y) = X*Y

Ansh777 · Answer

We know that:
Product of two Numbers= LCM*HCF

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

Answer: B

CrackverbalGMAT · Answer

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!

bumpbot · Answer

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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

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