  The physical origin of the >0.1 GeV emission detected from Gamma-Ray Bursts
(GRBs) by the Fermi satellite has not yet been completely understood. In this
work we consider the GeV light curves of ten GRBs with measured redshift
detected by the Fermi-LAT. These light curves are characterised by a long-lived
($\gtrsim10^2$ seconds) emission, whose luminosity decays in time as a
power-law. While the decay rate is similar for all GRBs (i.e. $L_{LAT}\propto
t^{-1.2}$), the normalisation spans about two orders of magnitude in
luminosity. However, after re-normalising the luminosities to the prompt
energetics $E_{iso}$ the light curves overlap. We consider the scenario in
which the temporally extended LAT emission is dominated by synchrotron
radiation from electrons accelerated at the forward external shock. According
to this model, at high-energies (i.e. above the typical synchrotron
frequencies) a small dispersion of the $E_{iso}$-normalised light curves is
expected. The fact that the LAT temporally extended emission follows this
behaviour reinforces its interpretation in terms of afterglow radiation from
external shocks. Assuming this scenario, we argue that the parameters
$\epsilon_e$ and $\eta_\gamma$ (i.e., the fraction of shock-dissipated energy
gained by the electrons, and the efficiency of the mechanism producing the
prompt radiation, respectively) must be narrowly distributed.
