Thread: External direct product

I have been studying about external direct products in my abstract algebra class recently. Just wanted to know, how can the "possible orders" of the elements of an external direct product be determined without actually calculating orders, element wise?

Like how can one find the possible orders of elements of Z4*Z2 (external direct sum of Z4 and Z2) ?
Help will be appreciated.

I guess one can arrive at an answer for the maximum order for some element in Z₄ X Z₂.
Won't that be the l.c.m of 4 and 2?