The Large Magellanic Cloud (LMC) has a unique cluster formation history in that nearly all of its globular clusters were formed either ~13 Gyr ago or less than ~3 Gyr ago. It is not clear what physical mechanism is responsible for the most recent cluster formation episode and thus the mysterious age gap between the LMC clusters. We first present results of gasdynamical N-body simulations of the evolution of the LMC in the context of its Galactic orbit and interactions with the Small Magellanic Cloud (SMC), paying special attention to the effect of tidal forces. We find that the first close encounter between the LMC and the SMC about 4 Gyr ago was the beginning of a period of strong tidal interaction that likely induced dramatic gas cloud collisions, leading to an enhancement of the formation of globular clusters that has been sustained by strong tidal interactions to the present day. The tidal interaction results in the formation of a barred, elliptical thick disk in the LMC. The model also predicts the presence of a large diffuse stellar stream circling the Galaxy, which originated from the LMC.