For starts: "friction at the pulleys" is absolutely not an acceptable answer.
This is the reasoning I have deduced: the system is loaded and then unloaded. Thus you could take this in a Potential Energy direction i.e. at the start the gravitational potential energy of the small masses, m, is some value and then this changes as the larger mass M changes.
When you assume that energy is conserved: the gravitational potential energy of the smaller masses, m, should be equivalent as you pass the same values for M (i.e. the values you get going one way should ideally be the same as going the other way). The fact that they are not, however, suggests that energy from the system is being lost. The only way for energy to be lost is for there to be some other conversion process happening. The only possible conversion process that could be impacting the system is a frictional force, which must be situated at the pulleys.
Hope this clears things up.