CMO 1988 Problem 6

Let $n$ ( $n\ge 3$ ) be a natural number. Denote by $f(n)$ the least natural number by which $n$ is not divisible (e.g. $f(12)=5$ ). If $f(n)\ge 3$ , we may have $f(f(n))$ in the same way. Similarly, if $f(f(n))\ge 3$ , we may have $f(f(f(n)))$ , and so on. If $\underbrace{f(f(\dots f}_{k\text{ times}}(n)\dots ))=2$ , we call $k$ the "length" of $n$ (also we denote by $l_n$ the "length" of $n$ ). For arbitrary natural number $n$ ( $n\ge 3$ ), find $l_n$ with proof.