If the product of two positive integers is 540, which of the following

Question

If the product of two positive integers is 540, which of the following can be the least common multiple and the greatest common divisor respectively of the two integers?

I. 108 and 5
II. 90 and 6
III. 27 and 20

A. I only
B. II only
C. III only
D. I, II and III
E. None of the above

GMATinsight · Accepted Answer

PROPERTIES :
1) LCM * HCF of two number a and b  = a*b 
2) LCM is always a MULTIPLE of HCF

Given:  a*b = 540

I. 108 and 5  - NOT POSSIBLE because 5 is not a factor of 108 
II. 90 and 6  - POSSIBLE because 6 is a factor of 90 and 90*6 = 540 
III. 27 and 20  - NOT POSSIBLE because 20 is not a factor of 27

ANswer: Option B

RaghavKhanna

RaghavKhanna · Answer

Let the two numbers be A and B

LCM (A,B) * HCF (A,B) = A*B

A*B = 540 (given)

All three options satisfy this condition.

Hence, answer: D

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yashikaaggarwal · Answer

The product of two no. = 540
Let the no. Be X and Y
X*Y = 540 = 2^2*3^3*5

The least LCM will be when the no. Have equal factors. 
For ex LCM of 10,10 is 10
Whereas 10&13 = 130

We have to bifurcate 2^2*3^3*5 into two parts with equal no. of factors.
Let, X = 2*3*5 and Y = 2*3*3
L.C.M will be 2*3*3*5 = 90 --------(1)

The Greatest HCF will be when the no. Have equal factors 
For ex HCF of 10,10 is 10
Whereas 10&13 = 1

We have to bifurcate 2^2*3^3*5 into two parts with equal no. of factors.
Let, X = 2*3*5 and Y = 2*3*3
H.C.F will be 2*3 = 6 --------(2)

L.C.M , H.C.F = 90,6
Option B is satisfying both
Answer is B

Posted from my mobile device

Anki1405 · Answer

If the nos. have equal no. of factors is the criteria then on taking X= 2^2*3 and Y= 3^2*5 , We should get the same result. But that is not the case

yashikaaggarwal · Answer

I know that, I just used that example to prove a point. not a part of solution. For example is written there as well

AstroNut · Answer

Answer B

540 = 2^2 x 3^3 x 5^1

540 is a product of 2 numbers . Now since power of 5 is 1, it can be part of only one of these 2 numbers. So under no circumstance 5 or its multiples can be GCD of these 2 numbers as in that case both numbers should have 5 as one of the multples.

Option I - GCD is 5 - Both numbers cannot have 5 in them
Option III - GCD is 20 = 5X4 - Both numbers cannot have 5 in them. This also cannot happen as 4 can be written as 2^2, which means both numbers need to have 2^2 , but 540 contains only one 2^2, not possible.

There is only one option (II) where GCD is not a multiple of 5. We don't need to look at anything else.

bumpbot · Answer

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If the product of two positive integers is 540, which of the following

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If the product of two positive integers is 540, which of the following

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