Triangle $ABC$ has altitudes $\overline{AD},$ $\overline{BE},$ and $\overline{CF}.$ If $AD = 12,$ $BE = 20,$ and $CF$ is a positive integer, then find the largest possible value of $CF.$
See a similar problem with heureka's answer here
https://web2.0calc.com/questions/geometry_136
+357 
