Problem Solving

tamiri wrote: 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