The sale began Tuesday and lasts through 11:59 p.m. on Jan. 25. The deals only apply to select dates for certain domestic and international flights.
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The prices apply to Southwest's "Wanna Get Away" fare class.
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In addition to the $40 fare from Los Angeles to Las Vegas, the sale also features one-way tickets from L.A. to San Francisco starting at $59.
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Internationally, the sale offers one-way tickets from L.A. to Cabo San Lucas starting at $119, and L.A. to Cancun starting at $180.
For more information, visit www.southwest.com/html/promotions.
KTRK-TV contributed to this report.