Proof Writing & Problem Solving · Superchallenge problem

The Euclidean algorithm on a pair $a > b > 0$ repeatedly replaces $(a, b)$ by $(b, r)$, where $r$ is the remainder of $a$ divided by $b$, stopping when a remainder is $0$; each division counts as one step. What is the smallest $a$ for which some $b < a$ makes the algorithm take exactly $10$ steps?