Liftmaster "magic" remote devices:
Liftmaster makes a somewhat universal remote control and a keypad that will program most Liftmaster/Chamberlain/Craftsman garage door operators (gdo's) as well as many of the most common other brands. They are able to do this because they transmit on five different frequencies simultaneously and   emulate the following different technologies:

• LiftMaster (All Models)
• CHAMBERLAIN (All Models manufactured after 1990)
• Sears CRAFTSMAN (All models manufactured after 1990)
• GENIE (All models manufactured after 1988)
• RAYNOR
• LINEAR
• MULTI-CODE
• STANLEY
• OVERHEAD DOOR (Machines Newer than 1995, aka Code Dodger)
• Wayne Dalton (372MHz Only) WILL NOT WORK FOR 303MHz Models
• Moore-O-Matic

The frequencies they transmit on are: 300, 310, 315, 318, 372, and 390 Mhz. 

The remote control is the 375LM/375UT(new version). The wireless keypad is the 387LM. Next time I will attempt to describe some basic aspects of programming these devices, because they can be daunting!

If you have any questions about whether these "magic" ("magic" is my word, noone else calls them that) remote devices will program to your specific gdo, call the kindly support staff at www.garagedoorsupplyco.com at 888-346-3173. They will help you sort it out, and if you feel inclined to buy from them, they are real good at providing tech support to their customers for their products --especially for programming your new remote device (and you won't have to be on hold nearly as long as the manufacturer's tech support lines).