There have been lots of recent posts about the crappy performance of LogMeIn on Macs. I had stopped using LogMeIn all together, till I found the solution (for me at least) given by PaulJi back in March in the thread "OS X browser plugin version 1.00.660 causes high CPU usage"
Revert from current plugin 1.00.660 to the old plugin v 1.00.562 by finding the old installer package (if you are lucky enough to have kept it) over the top of your current update
Spotlight search for npRACtrl.dmg on your cpu. Run it, overwrite your new version with the old, and instantly your back to rapid performance (I'm using Safari, and OSX 10.6.8 both ends)
Developers, extract your digit and sort this out!