Here is a look at how much it uses one one of my rigs with 7 1070's:

As you can see, I have 8 Gb but it uses less than 2 in REMOTE (no local display). I tend to buy HW that I can re-purpose in the event that mining goes south, so I recommend running a single 8 Gb stick per mining host. I typically purchase them as a 16 Gb "kit" with 2 8 GB DIMMs. Clearly, you could go as low as 4 with no issues but I have no use for DIMMs that small outside of mining.