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.
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