After final installation in the LHC tunnel, the MQM and MQY quadrupole magnets of the LHC insertions are now being commissioned to their nominal currents. These two types of magnets operate at 1.9 K and 4.5 K and with nominal currents ranging from 3600 A to 5390 A. From the very first acceptance tests of the bare magnets coming from the manufacturers, they have been powered using different cycles, in different configurations, at different temperatures and in different tests facilities. In this paper we present the global results of these powering tests. We aim at separating common from individual features of these groups of magnets. Temperature dependence of the training, temperature margin, and ultimate current can be extracted from these tests. As these magnets are used to match the optics and the dispersion in the machine, the projected ultimate current at which they can be operated is critical in view of operation of LHC.