US antitrust regulators required AMC, which is owned by China's Wanda Group, to sell its theaters in those markets to buyers to be approved by the Justice Department.
The cities, which include Peoria, Illinois and Madison, Wisconsin, are markets where AMC and Carmike are each other's most significant competition, the Justice Department said in a court filing.
"Moviegoers across the United States have benefitted from head-to-head competition between AMC and Carmike that has kept ticket prices in check," said acting attorney general Renata Hesse.
The Justice Department also required AMC to reduce its stake in National Cinemedia, a cinema advertising company, to avoid excessive concentration in the movie advertising business.
AMC called the DOJ's approval "the final regulatory hurdle" to closing the transaction to buy Carmike.
The agreement, which was signed by both the Justice Department and the companies, still needs court approval.
The transaction comes on the heels of AMC's USD 1.2 billion takeover of Europe's biggest movie theater, Odeon & UCI Cinema, which was finalized November 30.
After that purchase AMC dubbed itself the "largest movie exhibitor in Europe and the World."
Wanda has sought to transform its business in the face of uncertainties in Chinese real estate, and has invested heavily in entertainment assets.
Carmike shares fell 0.3 per cent, while AMC rose 0.5 per cent in midday trading.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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