The smallest possible values of x and y are 3 and 2, respectively. Most important is that 0 and 1 are impossible for both variables. Consider each choice to find one that must be a multiple of both x and y:
(A) Wrong. A number 1 greater than x cannot be a multiple of x (unless x = 1).
(B) Wrong. A number less than y cannot be a multiple of y.
(C) Wrong. Since y is positive, x - y is less than x. A number less than x cannot be a multiple of x.
(D) Wrong. xy is a multiple of both x and y, meaning that a number one less than xy cannot be a multiple of either. (Unless one of the numbers is 1, in which case it is a multiple of the variable that is equal to 1.)
(E) Correct! One example of variables that work here is x = 4 and y = 2. The LCM of 2 and 4 is 4, which is equal to (2)(4)/2.