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Loki is descendants of the frost giants

Laufey. He is the King of the Frost Giants, the biological father Loki. Odin is his step father.

Loki is from the family of frost giants and Odin has adopted Loki in a war with the frost giants

Loki is the biological son of Laufey. Odin adopted him.

lokis biological father is Laufey, the King of the Frost Giants. Odin adopted Loki after killing the king of the frost giants