  We theoretically study the Hall effect on interacting $M$-leg ladder systems,
comparing different measures and properties of the zero temperature Hall
response in the limit of weak magnetic fields. Focusing on $SU(M)$ symmetric
interacting bosons and fermions, as relevant for e.g. typical synthetic
dimensional quantum gas experiments, we identify an extensive regime in which
the Hall imbalance $\Delta_{\rm H}$ is universal and corresponds to a classical
Hall resistivity $R_{\rm H}=-1/n$ for a large class of quantum phases. Away
from this high symmetry point we observe interaction driven phenomena such as
sign reversal and divergence of the Hall response.
