Via product construction, create a DFA M, such that L(M)={anbmnormisamultipleof3} First create two machine: one where n is a multiple and one where m is a multiple of three. Then create the "union" machine. UPDATE: When I say create two machines, I mean an M1 and M2 such L(M1)={anbmnisamultipleof3}L(M2)={anbmmisamultipleof3}