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

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:

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

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)

Product of integers = LCM * HCF

Let the integer be a

Za = XY
a = XY/Z

IMO A

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

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