Stinkin' Pile of Money

Three men have a pile of money, their shares being \(\dfrac{1}{2}\), \(\dfrac{1}{3}\) and \(\dfrac{1}{6}\). Each man takes some money from the pile until nothing is left. The first man then returns \(\dfrac{1}{2}\) of what he took, the second \(\dfrac{1}{3}\) and the third \(\dfrac{1}{6}\). When the total as returned is divided equally among the men, it is found that each receives what he was originally entitled to. How much money was in the original pile, and how much did each initially take? [Find the smallest positive integer solution.]

Flos, Leonardo of Pisa, 1225

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