I am trying to prove the following Euclidean Algorithm but unable to locate a similar reference.

Question: Given two numbers $m,n$, what is the maximum number of steps that will be required to find the GCD using the Euclidean Algorithm?

I was considering proving this question using Lame's Theorem but wasn't sure if that is correct. Please assist me.


closed as off-topic by Namaste, Leucippus, The Phenotype, JonMark Perry, Parcly Taxel Feb 26 '18 at 17:30

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  • $\begingroup$ Please state Lame's theorem and include some more details otherwise your question would get closed. This is your first time that's why I am not going to close the question. $\endgroup$ – user152715 Feb 26 '18 at 11:09
  • $\begingroup$ Have a look at some of the questions listed under Related to see whether what you want to know is already given. $\endgroup$ – Gerry Myerson Feb 26 '18 at 11:58
  • $\begingroup$ Thank you for your responses. The question posed is what was given to me to prove without any other additional information which is why I need assistance. Under Related another user asked a similar question and someone pointed out Euclid's algorithm can never be more than five times the number of its digits (base 10). Would this be a good starting point? $\endgroup$ – MathStudent2 Feb 27 '18 at 2:26