How to select the order of LPC to model formants?
Usually you use 2 complex conjugate poles for each spectral peak. By other words, the order of the LPC model should be the double of the spectral peaks you want.
If you have 3 formants then you should use, at least, a 6th order LPC model.
You can try this yourself: record some vowels and then try (for each vowel) to use matlab or python to plot an LPC based spectrum. Change the order of the model to see if it can mimic the original spectrum.