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We report the recent measurements of the inclusive J/{\psi} production in ppcollisions at \sqrt{s} = 2.76 TeV, in pp collisions at \sqrt{s} = 7 TeV and inPb-Pb collisions at \sqrt{s_{NN}} = 2.76 TeV with the ALICE detector at theLHC. The J/{\psi} mesons are detected down to pT = 0 GeV/c via their di-muondecay channel at forward rapidity (2.5 < y < 4) and via their di-electron decaychannel at mid-rapidity (|y| < 0.9). A special emphasis is put on the nuclearmodification factor which is compared to the predictions of current J/{\psi}production models.

J/{\psi} production in pp collisions and in Pb-Pb collisions at the LHC with the ALICE experiment