A recently proposed lipid-chaperone hypothesis suggests that free lipid molecules, not bound to membranes, affect the aggregation of amyloidogenic peptides such as amyloid-β (Aβ) peptides, whose aggregates are the hallmarks of Alzheimer's disease. Here, we combine experiments with all-atom molecular dynamics simulations in explicit solvent to explore the effects of neuronal ganglioside GM1, abundant in mammalian brains, on the aggregation of two principal isoforms of Aβ, Aβ40 and Aβ42. Our simulations show that free GM1 forms stable, highly water-soluble complexes with both isoforms, and nuclear magnetic resonance experiments support the formation of well-ordered, structurally compact GM1+Aβ complexes. By simulation, we also show that Aβ40 monomers display a preference for binding to GM1-containing hetero-oligomers over GM1-lacking homo-oligomers, while Aβ42 monomers have the opposite preference. These observations explain why GM1 dose-dependently inhibits Aβ40 aggregation but has no effect on Aβ42 aggregation, as assessed by thioflavin T fluorescence.