  We consider the 0.1-10 GeV rest frame light curves of 10 GRBs detected by LAT
and with known redshift. In all cases the emission persists after the prompt
has faded away. This extended emission decays in time as a power-law. The decay
slope is similar among different bursts, while the normalization spans more
than 2 decades. However, when the LAT luminosity is normalized to the 1 keV-10
MeV energetics of the prompt emission E_iso all light curves become consistent
with having the same normalization, i.e. they cluster. At each given time the
ratio between the LAT luminosity and the prompt energetics is narrowly
distributed. We argue that this result is expected in the external shock
scenario and it strengthens the interpretation of the GeV emission in terms of
radiation from external shocks. In this context, we derive limits on the
distribution of epsilon_e (the fraction of the shock energy that goes into
electrons) and eta (the efficiency of the mechanism producing the prompt).
