  We examine the supersymmetry (SUSY) reach of the CERN LHC operating at
$\sqrt{s}=10$ and 14 TeV within the framework of the minimal supergravity
model. We improve upon previous reach projections by incorporating updated
background calculations including a variety of $2\to n$ Standard Model (SM)
processes. We show that SUSY discovery is possible even before the detectors
are understood well enough to utilize either $E_T^{\rm miss}$ or electrons in
the signal. We evaluate the early SUSY reach of the LHC at $\sqrt{s}=10$ TeV by
examining multi-muon plus $\ge4$ jets and also dijet events with {\it no}
missing $E_T$ cuts and show that the greatest reach in terms of $m_{1/2}$
occurs in the dijet channel. The reach in multi-muons is slightly smaller in
$m_{1/2}$, but extends to higher values of $m_0$. We find that an observable
multi-muon signal will first appear in the opposite-sign dimuon channel, but as
the integrated luminosity increases the relatively background-free but
rate-limited same-sign dimuon, and ultimately the trimuon channel yield the
highest reach. We show characteristic distributions in these channels that
serve to distinguish the signal from the SM background, and also help to
corroborate its SUSY origin. We then evaluate the LHC reach in various
no-lepton and multi-lepton plus jets channels {\it including} missing $E_T$
cuts for $\sqrt{s}=10$ and 14 TeV, and plot the reach for integrated
luminosities ranging up to 3000 fb$^{-1}$ at the SLHC. For $\sqrt{s}=10$ TeV,
the LHC reach extends to $m_{gluino}=1.9, 2.3, 2.8$ and 2.9 TeV for
$m_{squark}\sim m_{gluino}$ and integrated luminosities of 10, 100, 1000 and
3000 fb$^{-1}$, respectively. For $\sqrt{s}=14$ TeV, the LHC reach for the same
integrated luminosities is to $m_{gluino}=2.4,\3.1, 3.7$ and 4.0 TeV.
