Question 127
Let the three sides of a triangle be integers $l$, $m$, $n$, respectively, satisfying $l \gt m \gt n$ and $\{\frac{3^l}{10^4}\} = \{\frac{3^m}{10^4}\} = \{\frac{3^n}{10^4}\}$, where $\{x\} = x - [x]$ and $[x]$ denotes the integral part of the number $x$. Find the minimum perimeter of such a triangle.