I have found that the two patents placed on the RC6 algorithm are U.S. Patent 5,724,428 and U.S. Patent 5,835,600, but I'm having trouble determining the earliest date at which they will have both expired. Could anyone shed some light on this?
Pat. 5,724,428 expired on Nov. 1, 2015.
Pat. 5,835,600 is a DIVISION of this patent (not a continuation of it, as another responder indicated) and will expire on April 21, 2017.
You can refer to USPTO's patent term calculator.
You need to visit USPTO PAIR to see history of both patents. Some relevant data:
The application for Pat. 5724428 is 08/548,318, filed on 11-01-1995.
The application for Pat. 5835600 is 08/845,210, filed on 04-21-1997, and is a continuation of the application above.