Number of different longest common substrings
Let $\ell$ be the length of the longest common substring. The number of longest common substrings $m$ is at most
$$ m \leq \min(k^\ell,n-\ell+1). $$
Let $x = \log_k n$. If $\ell \leq x-1$ then $m \leq n/k$. Otherwise, $m \leq n-\log_k n+2$. One checks that the latter bound is always worse, and so $m \leq n-\log_k n+2$.