qa is 11

This is a good question. Where did you get it from ?
I too would be interested in finding out the best way to solve this. Looking forward to see what response some of the moderators/GMAT instructors will give to this post.

Too easy question. Remember in such question, try to simplify the equation first.

Let me write the equation and then we will simplify it:-

{(2^3) X (3^3) X (5)} + {(2^2) X (3^2) X (5^2)}

Take out the common factors from the above equation i.e. 2^2, 3^2 and 5

So it will become,

(2^2) X (3^2) X (5) X { (2 X 3 X 1) + (1 X 1 X 5) }

(2^2) X (3^2) X (5) X ( 6 + 5 )

(2^2) X (3^2) X (5) X (11)

So you can check 11 is highest prime factor among 2, 3, 5 and 11.

the source was scoretop and these questions are generally harder. SO basically what I am learning is that we need to simplify first ( key to many questions) then extract the common terms and the answer will be in the addition of the EXTRA terms. correct?!

Yup