Reachability of inequalities from Lame's theorem

In this paper, the following result is proved. The number of steps in Euclid's algorithm for two natural arguments, the smaller of which has $v$ digital digits in the decimal system, does not exceed the integer part of the fraction \linebreak $(v+ \lg ({\sqrt{5}}/ {\Phi}))/ \lg \Phi$, where $\Phi=(1+\sqrt{5})/2$, and this estimate is achieved for every natural $v$. It is also proved that partial or asymptotic reachability is valid for the other two known upper bounds on the length of the Euclid algorithm.