This is pretty difficult to determine without written sources. There are some sources like the Codex Mendoza and the Florentine Codex that refer to Mexica/Aztec conquests in the 14th and 15th centuries and many after-the-fact accounts of the substantial Inca conquests of the mid-15th century. Wikipedia can give you a run-down of the main Inca battles, and some of them seem to have been quite large, but the Incas did not have a system of writing (Quipu has not been shown to have been used for sounds, but research is ongoing), so the accuracy of the later accounts must be considered.