It's a 291 caliber and matches a picture off of the Longines website plus a few other forums online. Here the issue: the rotor doesn't do a great job of winding the ratchet wheel. If I wind it manually it will run; don't know how well, and its need a cleaning I am sure.

Brand: Longines
Type: Wristwatch
Department: Adult unisex
Movement: Mechanical (Automatic)
Model: Longines Conquest
With Original Box/Packaging: No
Year Manufactured: 1966
With Papers: No
Country/Region of Manufacture: Switzerland
Display: Analog
Vintage: Yes