RU-ALLRUSSIAN 1971 Problem 5

You are given three positive integers. A move consists of replacing $\mathrm{m}\leq \mathrm{n}$ by $2\mathrm{m}$ , n- m. Show that you can always make a series of moves which results in one of the integers becoming zero. [For example, if you start with 4, 5, 10, then you could get 8, 5, 6, then 3, 10, 6, then 6, 7, 6, then 0, 7, 12. ]