Neither of the picks originally belonged to the teams trading them; the selection sent to Montreal was the Arizona Coyotes' and the pick going to Los Angeles came from the Calgary Flames.
Thompson has suited up in 53 games for the Kings this season, recording four points in 12:55 per contest while winning 53 percent of his draws. He'll likely slot in as the Canadiens' fourth-line center.
The 34-year-old carries a cap hit of $1.65 million before hitting unrestricted free agency at season's end.
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