Tougher bullet construction and shot placement are the most important factors. I can think of worse cartridges for elk than a .30 cal controlled expansion bullet starting out at 2400 fps. Within 50-75 yards, a good 7.62x39 load will have similar energy to a 30/06 load has remaining at 300 yards, albeit with a lighter bullet. A 150 grain .311 bullet like the Sierra Pro Hunter will have a lower starting velocity more like 2150-2200 fps.
I use Hornady 123 grain SST bullets @ 2400 fps. for the smaller whitetails found in the valleys here, but would not use it for elk, I prefer at least 308 for that.
Montana has no restrictions on caliber for big game as long as it's a centerfire round. One could legally use a .22 Hornet if they desired, but I doubt anyone does. If it were a problem of people being undergunned, I'm sure the FWP commission would change the regulations.
Proper placement of a decent bullet from a 7.62x39 carbine would do the job on an elk, better than a less than optimal shot with a larger caliber. There is a lot of debate over what cartridge is the best for elk, deer, etc. but it usually all comes down to skill at shot placement, taking shorter shots instead of across the canyon ones, and selecting a bullet that gives a blend of adequate penetration and controlled expansion.
That being said, I would prefer at least something like a 7mm-08 or .308 for the bigger members of the deer family.