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Computing power is always an issue. Note that with an 8 core machine, it is very easy to simulate quickly hundreds of thousands of LHC collisions on your own machine for physics studies. I don't do this everyday, but almost (this is actually within my field of expertise) :)

EDIT: Note that this is not because it is easy that we don't need more computing power. Easy processes are easy to simulate, but we also need to simulate harder processes, we sometimes needs billions of simulated collisions and experimentalists often need to include an accurate simulation of the detector (which is very demanding in terms of CPU power).