The A340 only requires thrust in the 30-35,000lbs range for the -200 and -300 models hence they utilise the CFM 56-5C2 (31,200lbs) or the 56-5C3 (32,500lbs) or the 56-5C4(34,000lbs). The A330 for obvious reasons requires much more so RR Trent 772 is used (71,100lbs).
The A340-600 may well use RR engines as it's RTOW will approach that of the 747.
There...now i feel like a complete smartarse!
This info won't do anyone any good of course because we know you won't be turning up right????