I don't understand why you would say "Je leur ai acheté" rather than "Je les ai acheté." Isn't that a direct object, the thing being bought?
The two sentences have a different meanings.
Je les ai acheté.
Indicates that you buy something (les), so it could be translated like "I've bought them"
Je leur ai acheté
Indicates that you buy something from somebody (leur), so it could be translated like "I've bought from them."
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Je leur ai acheté peut vouloir aussi dire qu'on a acheté quelque chose pour quelqu'un (des enfants par exemple). – SdaliM May 11 '18 at 13:32
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