Best integer solution to overdetermined linear system with full column rank

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I have this impossible system and would like to have an aproximate solution through the least square method, but i'm having some problems figuring what to do, so i followed some guide on my book and got a solution, but i don't fully trust what i got.

$$2N+M=8$$ $$N+M=6$$ $$3N+M=5$$ $$N+3M=12$$ ps: I'm lacking skills to make this look like a system, but it is a system of 4 equations.

N and M are restricted to being integers

Well, i got $$N=128/33$$ and $$M=279/297$$ but it seems kind off.

Thanks in advance