A theorem due to the French mathematician and engineer Gabriel Lam\'e (1795-1870) establishes an upper bound for the number of divisions required in the Euclidean GCD algorithm. Namely, the number of divisions required to find GCD[a,b] is less than or equal to five (5) times the number of digits of Min[a,b]. Lam\'e's theorem appeared in
Note sur la limite du nombre des divisions, C. R. Acad. Sci. Paris Ser. A-B 19 (1844), pp. 867-869.
It is viewed by many as the first published analysis of the ``running time'' of a number theoretic algorithm (implying that Euclid's algorithm runs in polynomial time).