Did some hunting in my youth on the Eastern slope of the Canadian Rockies. Never managed to get an elk in my sights, but my dad and his buddies used .308 Win and .303 British. (Dad was in the Canadian army and they were used to the .303 from WW2 and Korea, and 7.62x51 NATO in their FN/FAL rifles).
I don't know what bullets they used, they were all factory loads, no reloading by anybody. And more than once we were eating elk via .303 BR and .308 Win. My dad called his Husqvarna .308 lightweight his "elephant" gun, saying he would be fine taking it elephant hunting. BTW he was a trained sniper.
My first centerfire rifle was a Parker Hale sporter .303 BR, and I was confident to shoot anything from a whitetail to a moose at the time. We could get tags for deer, elk, woodland caribou, moose, and black and grizzly bears in those days (mid '60s).
By the way Spanky ,one of the things you will find out about elk is that they are delicious.