  We investigate the variability properties of blazars in the GeV band using
the data of the Fermi/LAT telescope. We find that blazars exhibit variability
on the scales down to the minimal timescale resolvable by Fermi, which is a
function of the peak photon count rate in the LAT. This implies that the real
minimal variability timescales for the majority of blazars are typically
shorter than those resolvable by the LAT. We find that for several blazars
these minimal variability timescales reach those associated to the blazar
central engine, the supermassive black hole. At the same time, none of the
blazars exhibits variability on the timescale shorter than the black hole
horizon light crossing time and/or the period of rotation around the last
stable circular orbit. Based on this fact, we argue that the timing properties
of the gamma-ray signal could be determined by the processes in the direct
vicinity of the supermassive black hole.
