The math involved is elementary algebra, but making sure you put all the variables in the right spot is a little tedious.
Just off of headmaths (I hope I executed the ops right), it's like 213 with just 100heavy armor, and no smithing improvements.
Without smithing, you'll have to get all 5 Juggernaut and utilize The Whole set + Matching set, bringing it to around 538 total. (-100 for the hidden +25 Armor effect on each piece equipped)
Note, these roughish estimations are without a shield.
Without any Smithing at all, I think only Daedric can hit the cap.*
*You can also fortify your Armor skill through enchantments, depending on how much you add, Dragonplate or Ebony can also reach the 567(Displayed) Cap.