I had 2 Dcs, 16 months apart so not quite the same but....
My lifesavers were,
a Huge playpen, actually several playpen sections locked together that took over the living room ( about 10ft diameter) on a big thick rug, all toys in there.
Life happened within the playpen, Games, soft books etc.
Tv visible on a shelf outside so could be put on but not reached, Nappies and wipes and bin on a stand outside playpen but reachable from within.
Nothing else they may like to touch outside on view, as too tempting to escape, basically empty room! I even has a small comfortable soft armchair in the Playpen.
When I needed to leave and cook etc, put washing on, l would put on favourite videos for immediate distraction, then turn off on returning. so it was always a treat.
Also you can link or tie babygates together to block off entire areas of the house if open plan.
I also had stairgates every where, ie bathroom doorway, so l could plonk them on a pile of towels whilst having a shower etc. Or plonk them in the bedroom playpen whils getting dressed ( I also had smaller playpens upstairs with a stash of interesting things, to keep them occupied for 30 minutes) If they hurt each other then seperate them.
I never subscibed to the point of view that its fun to restack the kitchen cupboards 7 times a morning! so the kitchen was out of bounds until they were older unless they were sitting at the table strapped in.
Good Luck!