Testing the ability of climate-ice sheet coupled models to simulate past ice sheets and climates can provide a way to evaluate the models. One example is the Last Glacial Maximum (LGM), when huge ice sheets covered the Northern Hemisphere, especially over the North America. Here, we perform 200 ensemble member simulations of the North American and Greenland ice sheets and climate of the LGM with an ice sheet-atmosphere-slab ocean coupled model Famous-BISICLES. 16 parameters associated with climate and ice dynamics are varied. The simulated results are evaluated against the LGM global temperature, the total ice volume and the ice extent at the southern margin of the North American ice sheet. In the ensemble simulations, the global temperature is controlled by the combination of precipitation efficiency in the large-scale condensation and entrainment rate in the cumulus convection. Under reasonable LGM global temperature, we find that the surface albedo and Weertman coefficient in the basal sliding law control the North American ice volume. In contrast, the ice volume of Greenland is found to be controlled by the Weertman coefficient. Based on the constraints, the model produces 6 good simulations with reasonable global temperature and North American ice sheet. We also find that warm summer surface temperature biases at the ice sheet interior as well as downscaling of surface mass balance based on altitude can cause strong local ice melting. This implies the need of better representing the atmospheric conditions and surface mass balance in the ice sheet interior.