The greatest common factor of two positive integers is X. The least co

Question

The greatest common factor of two positive integers is X. The least common multiple of these two integers is Y. If one of the integers is Z, what is the other?

A. XY⁄Z
B. XZ + YZ
C. X⁄Z + Y
D. X + Y⁄Z
E. X + Z⁄Y

BrentGMATPrepNow · Accepted Answer

--------ASIDE----------------------
There's a nice rule that says:
  (greatest common divisor of A and B)  (least common multiple of A and B)  =  AB  
 Example : A = 10 and B = 15
Greatest common divisor of 10 and 15 =  5 
Least common multiple of 10 and 15 =  30 
Notice that these values satisfy the above rule, since ( 5 )( 30 ) =  (10)(15) 
--------BACK TO THE QUESTION! ----------------------

One of the two integers is Z  
Let the other integer be Q. 
So,  our goal is to determine the value of   Q

GIVEN:
 The greatest common factor (divisor) of Z and Q is X.  
 The least common multiple of Z and Q is Y.

Take the formula:   (greatest common divisor of A and B)  (least common multiple of A and B)  =  AB  
And plug in the given info to get:   (X)  (Y)  =  ZQ   
In other words: XY = ZQ

Divide both sides by Z to get: XY/Z = Q

Answer: A

Cheers,
Brent

EMPOWERgmatRichC · Answer

Hi All,

This question can be solved by TESTing VALUES. You just have to pay careful attention to what each variable represents (and the VALUE that you choose for each).

We're told that the greatest common factor of two positive integers is X and the least common multiple of these two integers is Y. We're then told that one of the integers is Z and we are asked to find the OTHER integer.

IF....
the two integers are 2 and 3,
then the GCF = 1 and LCM = 6
So...
X = 1
Y = 6
Z = 2

We're looking for an answer that equals 3.

A. XY⁄Z = 6/2 = 3 This is a MATCH
B. XZ + YZ = (1)(2) + (6)(2) = 10 NOT a match
C. X⁄Z + Y = 1/2 + 6 = 6.5 NOT a match
D. X + Y⁄Z = 1 + 6/2 = 4 NOT a match
E. X + Z⁄Y = 1 + 2/6 = 1 1/3 NOT a match

Final Answer:  A

GMAT assassins aren't born, they're made,
Rich

Praveengeol · Answer

Say other integer is W

Formula 
GCF(W&Z)*LCM(W&Z) = W*Z

X*Y = W*Z
So W= XY/Z

Answer A

hoang221 · Answer

Key point to remember: The greatest common factor * least common multiple of integer A and B will equal A*B (only applicable to 2 integer)

Denote the other integer as k, we got  X*Y = Z*k => k = \frac{(X*Y)}{Z}  (A)

Kinshook · Answer

Product of integers = LCM * HCF

Let the integer be a

Za = XY
a = XY/Z

IMO A

BrushMyQuant · Answer

Given that GCD of two positive integers = 3 and LCM of two positive integers = Y and one number is Z and we need to find the value of other integer

Theory:  LCM of two Numbers * GCD of two numbers = Product of the numbers

=> LCM * GCD = Z * T (Assume T is the other integer)
=> Y * X = Z * T
=> T =  \frac{XY}{Z}

So,  Answer will be A 
Hope it helps!

To learn more about LCM and GCD watch the following videos

https://www.youtube.com/watch?v=7jPV6JD0908

https://www.youtube.com/watch?v=vtSsAjcF-0Y

bumpbot · Answer

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