We use a state-of-the-art ocean general circulation and biogeochemistry model to examine the impact of changes in ocean circulation and biogeochemistry in governing the change in ocean carbon-13 and atmospheric CO₂ at the last glacial maximum (LGM). We examine 5 different realisations of the ocean's overturning circulation produced by a fully coupled atmosphere-ocean model under LGM forcing and suggested changes in the atmospheric deposition of iron and phytoplankton physiology at the LGM. Measured changes in carbon-13 and carbon-14, as well as a qualitative reconstruction of the change in ocean carbon export are used to evaluate the results. Overall, we find that while a reduction in ocean ventilation at the LGM is necessary to reproduce carbon-13 and carbon-14 observations, this circulation results in a low net sink for atmospheric CO₂. In contrast, while biogeochemical processes contribute little to carbon isotopes, we propose that most of the change in atmospheric CO₂ was due to such factors. However, the lesser role for circulation means that when all plausible factors are accounted for, most of the necessary CO₂ change remains to be explained. This presents a serious challenge to our understanding of the mechanisms behind changes in the global carbon cycle during the geologic past.