Would this work? Taking China tour.

Hey, I'm leading a small group of teachers from the U.S.A. on a China tour, and was hoping not to have to pay for the expensive multiple entry visas, since we will only go this one time. If we go from LAX to PVG, stay for 72 hours, then fly to HKG, stay for 3 days, then fly straight to PEK, stay for 72 hours, then fly back to LAX....Could we avoid having to purchase visas?

Thanks!