EAF:
NJW is correct: with a 20 round 5.56 x 45mm magazine, you can only load it with 8 rounds of 7.62 x 39mm. Military surplus magazines would work just fine. All AR-15 lower receivers are basically the same regardless what is marked on its side.
You can always get your upper rebarreled in 5.56 x 45mm. If you like the 7.62 x 39mm cartridge so much, you can always get another upper receiver that is barreled for the 5.56, that way, you can use two calibers just by swapping the upper receivers, while using the same magazine and lower receiver.
Johannes