Does Newtonian $F=ma$ imply the least action principle in mechanics?

I've learned that Newtonian mechanics and Lagrangian mechanics are equivalent, and Newtonian mechanics can be deduced from the least action principle.

Could the least action principle $\min\int L(t,q,q')dt$ in mechanics be deduced from Newtonian $F=ma$?

Sorry if the question sounds beginnerish

Answer

You also need an expression for the Lagrangian, which in classical mechanics is

$$L = T - U$$

Where $T$ is the kinetic energy and $U$ is the potential energy.

Provided that you can associate a potential $U$ to the force $\vec{F}$ such that $\vec{F} = - \vec{\nabla} U$ (such a force is said to be conservative), the principle of least action and Newton second's law are equivalent.

The demonstration for a single particle in 1D ($T = m v_x^2 /2$, $F = -dU(x)/dx$) is actually a good exercise.