Three non-collinear lattice points $A,B,C$ lie on the plane $1+3x+5y+7z=0$. The minimal possible area of triangle $ABC$ can be expressed as $\frac{\sqrt{m}}{n}$ where $m,n$ are positive integers such that there does not exists a prime $p$ dividing $n$ with $p^2$ dividing $m$. Compute $100m+n$.

[i]Proposed by Yannick Yao[/i]