what KIND of structure are you generating? we're not mind-readers. and what is (15)? notations vary, do you mean the ideal of integers generated by 15, or the group (Z15,+), or a residue class of 15 modulo some integer, or the integer 15? you might mean any of these things.
my guess is you mean the principal ideals generated by 15 and 243, in which case you want the smallest ideal of (presumably Z) that contains (15) and (243). wouldn't any element of that have to be of the form 15a + 243b? can you think of a simpler description?