Less than a hundred years.

The Inca and Aztec empires developed in the Americas from around the same date, the 1430's. They both conquered vast areas of territory in a very short time and ruled over millions of subjects- At the peak of their power the Aztecs had about ten million persons under their control, the Inca about twenty million.
The method of conquest of both empires was as ruthless as their autocratic ruling style- Human sacrifices and torture were part of both the Inca and Aztec states. The victims used in the sacrifice were prisoners belonging to the defeated nations conquered by the empires, including men, women and children. At a single ceremony it is said that the Aztecs killed more than ten thousand sacrificial victims. 
There are many important and puzzling cultural characteristics shared by the Incas and the Aztecs. For example, there is proof that both had knowledge of the wheel and that both refused to use it in anything but children's toys. They also never used pack animals. Both cultures had myths about  the future arrival of white-skinned, bearded strangers that would bring about a new era.  All of this happened despite that, until today, there has not been any proof of communication between the Incas and the Aztecs.
The history of both empires was very short, so brief that in all of their history the Incas only had five emperors, the Aztecs eight. In the early 1520's the Spanish arrived in both empires, in each case they were welcomed as divine beings as per the prophecies.
The Aztecs and the Incas were destroyed at  the same time in a similar way. The Spanish invaders utilized cultures that had been conquered by each empire as foot soldiers to destroy their former rulers and  in both cases their emperors were taken as hostages and eventually murdered by the invaders. Which only proves one thing- Payback is a bitch.