Recall the Law of Moments for a one dimensional rod:
"When an object is in equilibrium the sum of the clockwise moments is equal to the sum of the anticlockwise moments."
I understand that we may define a quantity $F \times d$, and call it a moment. Then, experimentally, we can observe that $F_1\times d_1 = F_2\times d_2$ is a necessary condition for equilibrium.
However, is it possible to derive the Law of Moments from some more fundamental principle, e.g. the principle of least action?