- In a system with two heavy bodies there are 5 Lagrangian points. You can easily calculate the positions of L1, L2 and L3 yourself using Newton's law of gravity; L4 and L5 might be harder. When you add extra bodies (extra planets, moons, ...) the problem will only be solvable in very specific, easy cases.
 - When calculating these points you generally want to neglect the mass of the body in orbit, so you really don't want this mass to be bigger than about $1%$ of the bigger masses. 

[![Lagrangian points][1]][1]


  [1]: https://i.sstatic.net/LbZSQ.jpg