well since the Spanish conquered them in the 15 century i would guess about the 15th century late 14th at the most
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1325-1521
Around 1572, which is around the downfall of their civilization. Also try Wikipedia.
The Inca's lived from 1200 AD to late 1500 AD
The Spaniards led to the decline of the Inca civilization. The Spaniards took Atahualpa (ruler at the time,) hostage and killed his brother Huascar. Then they installed a new leader Atahualpa's brother, Manco Inca. He eventually passed on the throne to his son Tupac Amaru. When the Spaniards captured and executed him, the Inca's resistance to the Spaniards ended.
The Inca came around in about 1430 C.E. and fell in 1525 C.E. when they were conquered by the Spanish.