GCF, LCM, and Order of Operations

In my Basic Mathematics class we just finished discussing the order of operations, and students always seem to have a problem with it, especially when division comes before multiplication (Sally has always told them otherwise).  Today we discussed finding the Greatest Common Factor (GCF) and Least Common Multiple (LCM), another topic that students sometimes seem to have a problem with.  I came up with the following problem, which sparked quite a lot of discussion in the classroom.  But more than that, I think it is the type of problem that continues to reiterate the Order of Operations, and doesn’t back students into the hole of forgetting what they have learned from one chapter to the next.