Dear Bjones, the CFM56's on the 737 classic and KC-135R are not anywhere near the same engines. The CFM56-2 on the KC-135R has a 68 inch diameter fan and would never fit on a 737. The CFM56-3 on the 737 classic is only 60 inches.
The different versions of the CFM56, the -2, -3, -5 and -7, have four different fan diameters. Only the -2 and the -5A and 5B have identical fan diameters at 68 inches. The -3 is 60, the -5C is 72 and the -7 is 61 inches.
And there is a load of sub-variants with quite substantial differences including varying number of compressor and turbine stages. The largest CFM56, the -5C4, is almost twice as powerful as the smallest CFM56.
CFM56 is rather an engine family than an engine type. Have a look at http://www.cfm56.com