If m and n are positive integers such that m is a factor of

I don't think there is anything called 'the best approach'. Each person uses what works best for her/him. I jump to plugging in numbers whenever I see variables in the questions and variables in the options. I know that within 1 or 2 iterations, I should get my answer. I also like to choose the simplest possible numbers. e.g. here I would put m = 1 and n = 1 (both positive integers and m is a factor of n). But the moment I put them equal, I see that options d and e will be the same. So instead, I put m = 1 and n = 2. 2n = 4.
Number of positive multiples of 1 that are less than or equal to 4 = 4 (1, 2, 3, 4)
Only e gives me 4 when I put n = 2 and m = 1
Answer (E).

Mind you, it is not a good idea to plug in numbers when you have 3-4 variables since you might just get lost in them.