Billionaire investor Carl Icahn has bought a significant chunk of Metro-Goldwyn-Mayer Inc.'s debt and is pushing the beleaguered film studio to merge with rival Lions Gate Entertainment Corp., said people familiar with the matter.

Icahn, who is Lions Gate's largest shareholder with nearly 33 percent of shares, told people close to MGM earlier this week he holds somewhere between $400 million and $500 million of MGM's debt outstanding and is continuing to build his position in the studio, they said.

The purchases give Mr. Icahn about 10 percent of MGM's outstanding debt. In discussions with some MGM creditors earlier this week, Icahn said he believes MGM and Lions Gate could benefit from synergies, the people said.

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