Meson interactions at large $N_c$ from Lattice QCD

We report on the computation of the scaling of QCD observables with the number of colours, $N_c$. For this, we use dynamical configurations with four active flavours, $N_f=4$, and values of $N_c=3-6$. We study the meson masses and decay constants, and compute the leading and subleading contributions to the Low Energy Constants (LECs) of the chiral Lagrangian. We also explore $\pi \pi$ scattering in the $I=2$ channel, and compute the $K \to \pi$ weak decay matrix elements. We comment on the relation of the latter to $K \to \pi\pi$ processes and the $\Delta I=1/2$ rule.