Lamé's Theorem

Theorem
Let $a, b \in \Z_{>0}$ be (strictly) positive integers.

Let $c$ and $d$ be the number of digits in $a$ and $b$ respectively when expressed in decimal notation.

Let the Euclidean Algorithm be employed to find the GCD of $a$ and $b$.

Then it will take no more than $5 \times \min \set {c, d}$ cycles around the Euclidean Algorithm to find $\gcd \set {a, b}$.