LCM and GCM

[tamiri]

Could I have guide lines in solving that problem?

Thank you,
Tamir

If positive integers A and B have LCM of 150, what is their possible GCD?
a. 3
b. 7
c. 9
d. 20
e. 45

[Jim@StratusPrep]

The prime factors of 150 are 2, 3, 5 and 5.

The GCD must not contain any other factors.

A is the answer.

[Brent@GMATPrepNow]

If positive integers A and B have LCM of 150, what is their possible GCD?
a. 3
b. 7
c. 9
d. 20
e. 45

Here's another approach.

For GCD and LCM questions, it's useful to be able to think of pairs of values that have given GCDs or LCM's.

So, if we're told that A and B have a LCM of 150, what are some possible values of A and B?
Here are a few:
A = 150 and B = 150
A = 150 and B = 1
A = 150 and B = 10
etc.

Let's keep listing possibilities, and see if any have a GCD that matches one of the answer choices.

A = 150 and B = 150
GCD = 150
Not one of the answer choices. Keep trying.

A = 150 and B = 1
GCD = 1
Not one of the answer choices. Keep trying.

A = 150 and B = 2
GCD = 2
Not one of the answer choices. Keep trying.

A = 150 and B = 3
GCD = 3
YES, one of the answer choices.

Answer = A

Cheers,
Brent

[tamiri]

Jim,
9 has also 3,3
20 has 2,2,5
All these are factors that are in the LCM (2,3,5,5)
Tamir

[bubbliiiiiiii]

Another approach that works here is only A divides 150 among all options.

[randude]

Property :
LCM (A, B) x GCF ( A,B ) = A.B

150 x GCF ( A,B ) = A.B

GCF ( A,B ) = A.B / 150

This tells us, A.B must contain factors of 150 to be divisible by 150 i.e

150 = 2.3.5.5.....n

Now looking at the answer choices --- Only 3 can be formed from the prime factors of 150. Thus A is the correct answer