Victor's Level 5 Challenges - 2

Let the three sides of a triangle be integers l,m,nl,m,n with l>m>nl>m>n and satisfy the equation

{3l104}={3m104}={3n104} \large \left\{\frac{3^l}{10^4}\right\}=\left\{\frac{3^m}{10^4}\right\}=\left\{\frac{3^n}{10^4}\right\}

Find the minimum perimeter of such a triangle.

Details and Assumptions:

{x}=x[x]\{x\}=x-\left[x\right] and [x]\left[x\right] denotes the integral part of the number xx.

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