Of the elk I've shot the distance has been from 300 yards, the only one that far away, to 75 yards with most being under 200 yards.
Mostly used a 7mm Mag, with these other calibers tossed in; 30-06, 338-06, 35 Whelan, 45-70, .270 Win., 300 Win. Mag. but my favorite has to be the 7mm Mag for open country and the 1886 45-70 for timber humting.
The one elk shot with a .270 took a total of 5 rounds of 150 gr Hornadys as he made it to the timber on the far side of a meadow. Must admit the first shot was at 150 yards and was very poor placement on my part, this was a long time ago when I was just a pup.
Hope this helps.