The AR platform is limited by the dimensions of the magazine well. A 5.56 AR will take the .204, .223, 6.5 Grendel (rare), 6.8 SPC, or .30 AR. An .308 AR will take the .243, 260, 6.5 Creedmoor, 7mm-08, .308, and I've even seen them in .300 WSM. .270 and .30-06 are just too long - pure and simple. Also - note that the upper and lower need to match - in other words, you can't pin a longer AR-10 lower to a shorter AR-15 upper, or a shorter AR-15 lower to a longer AR-10 upper to gain the "benefit" of more chambering possibilities as I've seen posts here suggest in the past.

(edit) - I've put my 7-year-old daughter behind an AR carbine recently. It's a sandbag/benchrest proposition for her. Collapsible stock is great, but handguards too wide for her to really hold onto. No way is she carrying it much farther than from the truck to the bench. I've also had her behind a CZ527 Varmint in .223. That combo seemed far more manageable, incorporating a bipod. For some reason, LOP on that stock is shorter than LOP on the other 527 American I have. She's fine with it, but it's even heavier than the AR - and almost as long as she is tall.