LCM and GCF

[manik11]

If the least common multiple of integers x and y is 840, what is the value of x?

(1) The greatest common factor of x and y is 28.
(2) y = 168

OA : C

[GMATGuruNY]

RULE:
For any positive integers x and y, xy = (LCM of x and y)(GCF of x and y).

Statement 1:
Thus:
xy = (840)(28).

It's possible that x=1 and y=840*28.
It's possible that x=840*28 and y=1.
Since x can be different values, INSUFFICIENT.

Statement 2:
840=168*5.
It's possible that x=5 and y=168, with the result that the LCM of x and y is 840.
It's possible that x=168*5 and y=168, with the result that the LCM of x and y is 840.

Since x can be different values, INSUFFICIENT.

Statements combined:
Since xy = (840)(28) and y=168, x=(840/168)(28) = 5*28 =140.
SUFFICIENT.

The correct answer is C.

[OptimusPrep]

If the least common multiple of integers x and y is 840, what is the value of x?

(1) The greatest common factor of x and y is 28.
(2) y = 168

OA : C

Always remember x*y = LCM (x, y) * GCF (x, y)

Statement 1: GCF = 28
x*y = 840*28
We cannot say anything about x
INSUFFICIENT

Statement 2: y = 168
Clearly we cannot tell anything about x
INSUFFICIENT

Combining both the statements:
LCM = 840, GCF = 28 and y = 168
Hence we can find the value of x
SUFFICIENT

Correct Option: C