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It is mentioned in the Bhagwat Puran that Sri Krishn indeed have 16108 wives. The Srimad Bhagwat Puran mentions this in detail. Entire chapter is dedicated to this section in Bhagwat Puran Book 10.61 titled “A Glimps into the household life of Sri Krsna”. Below is a snippet of the entire Leela (Figure 1 to 5). Narad muni was wondering how Bhagwan Krishn was living with 16108 wives so in order to get the answers he visited Bhagwan to see for himself. After arriving, Narad Muni went around mansion to mansion and was shocked with what he was seeing. He saw that Bhagwan Krishn was present in each mansion with different wife. In every mansions where he entered he found Bhagwan was with each wife. So Bhagwan manifested himself into multiple forms to live as a household couple with each wife. He was doing many different tasks from doing Gayatri Mantra to playing with his children to giving charity and performing rituals. This is clear when you read the passage below Figure (1 to 5). Also read this article How many children did Bhagwan Krishn have?
