The Last Glacial Maximum (LGM) is characterized by huge ice sheets covering the Northern Hemisphere and by the cold climate due to weaker summer insolation and lower atmospheric CO₂. Here, we perform a 200-member ensemble of simulations of the North American and Greenland ice sheets and climate of the LGM with a coupled ice sheet-climate coupled model (Famous-BISICLES) to see how the ice sheets and climate are sensitive to uncertain parameters in the model. The simulated results are evaluated against the LGM global temperature, the total ice volume and the southern extent of the North American ice sheet. In the ensemble of simulations, the global temperature is controlled by the combination of parameters in the large-scale condensation scheme and the cumulus convection scheme. Under reasonable LGM global temperature, we find that the surface albedo controls the North American ice volume. In contrast, the ice volume of Greenland is found to be controlled by the basal sliding law. The results will be compared to a similar ensemble simulation under modern Greenland ice sheet and climate to explore a potential connection between the two periods.