Cute minimum sum

Put weights a,b,c on points A,B,C. The expression becomes the moment of inertia about P so it is minimum when P is the centre of mass which is precisely the Incenter because angular bisector of the vertex divides the opposite side in the ratio of its legs correspondingly. So the minimum value is $aAI^2+bBI^2+cCI^2$
$aAI^2=a (\frac{bc((b+c)^2-a^2)}{(b+c)^2}$ ( $\frac{(b+c)^2}{(a+b+c)^2}$ ))= abc ( $\frac{b+c-a}{a+b+c}$ )
$aAI^2+bBI^2+cCI^2=abc$
So the answer is 21x23x39=18837