@pC
Cross product is an approach to get Compound Automata.
But that does not always guarantees intersection. We need to check condition given in the question, i.e OR or AND . If it is OR like in this case, then Union is better to accept {0,4,5,8,10,12,15,16,20............}
and if AND is given, then intersection is better to accept {0,20,40,60,80,100,120,140.........}.