  The apparent unification of gauge couplings in Grand Unified Theories around
10$^{16}$ GeV is one of the strong arguments in favor of Supersymmetric
extensions of the Standard Model. In this paper, an analysis of the
measurements of the strong coupling running from the CMS experiment at the LHC
is combined with a "traditional" gauge coupling unification analysis using data
at the Z peak. This approach places powerful constraints on the possible scales
of new physics and on the parameters around the unification scale. A
supersymmetric analysis without GUT threshold corrections describes the CMS
data well and provides perfect unification. The favored scales are $M_{SUSY}\
=\ 2820\ +670\ -540$ GeV and $M_{GUT}\ =\ 1.05 \pm 0.06 \cdot 10^{16}$ GeV. For
zero or small threshold corrections the scale of new physics may be well within
LHC reach.
