to identify an aircraft engine it is best (IMHO) to look at both the aircraft type itself, and then look at the engine. it takes a bit of extra knowledge but it is a sure-fire way of identifying aircraft and their relative engine types.
for example.
the A340-300, as you mentioned, does not have a core exhaust system sticking out the back of its engines. this feature also appears on most CX 747s which use RB211-524 G/H-T engines. in this situation you should look at the aircraft type, that will give you the key to which engine it actually is. knowing the aircraft type and its associated engines will tell you that the 747 is not using the CFM56 but the RB211, and the Airbus is not using RB211 but CFM56. this is simply because the 747 does not have a CFM56 option, and neither does the A340-300 have a RB211 option.
it just takes a little research. good luck!
