Solution: Give a pile of candy to five people, four more, three more for four people and two more for three people. It can be said that this pile of candy is distributed to five people 1 block, four people 1 block and three people 1 block, which means that this pile of candy is at least the least common multiple of 5, 4 and 3.

So there are at least 59 pieces of candy in this pile.