Question:

Let $OA$, $OB$, $OC$ be coterminous edges of a cuboid. If $l,m,n$ be the shortest distance between the sides $OA$, $OB$, $OC$ and their respective skew body diagonals to them, then find $\dfrac{\left(\frac{1}{l^2}+\frac{1}{m^2}+\frac{1}{n^2}\right)}{\left(\frac{1}{OA^2}+\frac{1}{OB^2}+\frac{1}{OC^2}\right)}$