I too love to hunt elk! It's been awhile since my last big bull was taken but I still love those rocky mountains and being out there doing so.
I have used several calibers during those years, everything from a 25-06, 270 Win, 30-06, .300 Win mag, .338 Win mag and .375H&H
I don't advise anything smaller than the 30-06 for bull elk and 180 grain bullet.