  We show that the centrality dependence of the multiplicity is identical in
Pb+Pb and Xe+Xe collisions at the LHC, up to a constant factor. This geometric
scaling is revealed if one defines centrality according to impact parameter, as
opposed to the usual experimental definition, which is in terms of
multiplicity. We reconstruct the impact parameter dependence of the
multiplicity from experimental data using a recently-developed inversion
method, which turns out to describe ALICE Xe+Xe multiplicity data much better
than usual Monte Carlo Glauber fits. The multiplicity as function of impact
parameter extracted from ALICE data is compared to model calculations.
