In KY the .270 is the minimum legal caliber.

I normally deer hunt with a 7mm RM...which is more than enough for elk.

But if I had to select one rifle to hunt elk with (noting that elk live in rough areas sometimes inhabited by bears) I would go with a .338 Winchester Magnum.

The .340 Weatherby Magnum and the .338 Remington Ultra Mag would also get the job done on any elk, though no one local carries ammo for these rifles (have to order via Cabelas / BassPro)