As of my last knowledge update in October 2021, the three most populous cities in South America are:
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São Paulo, Brazil - This is the largest city in South America and one of the largest in the world, with a population of over 12 million people in the city proper and around 22 million in the metropolitan area.
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Buenos Aires, Argentina - The capital city of Argentina has a population of about 3 million in the city proper, with around 15 million in the metropolitan area.
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Rio de Janeiro, Brazil - Rio de Janeiro has a population of around 6.7 million in the city proper and about 13 million in the metropolitan area.
Population figures can change and should be verified against the most recent data for accuracy.