The following is an example of the type of question you might see on the GRE exam. It combines the topics of prime factorization and common multiples, two topics we have covered separately in other examples.

Two odd distinct integers p and q are selected such that these are more than 1 but less than 13. Which of the following numbers could be divisible by both p and q?

a. 70

b. 189

c. 396

d. 180

e. 182

Approach: Keep in mind that they are not asking about the number which should be divisible by all possible odd numbers between 3 and 11 (both included). Rather they are asking about what COULD be the numbers divisible by both.

So, we need to look for those numbers which are divisible by at least 2 odd numbers among 3,5,7,9, and 11.

Prime factorization of numbers would be helpful here.