Kim Kardashian and Lewis Hamilton Go Rug Shopping in L.A., See Pics

Kim Kardashian and Lewis Hamilton are fully in their cozy couple era ... so comfortable, they’re out here doing the most domestic thing possible -- rug shopping.

Check the pics ... the duo kept it low-key in L.A. Tuesday, dressed down while browsing luxury rugs ... just days after popping up together at Coachella.

Kim, of course, had her signature curves on full display in gray leggings and a cropped hoodie ... while Lewis matched the vibe, keeping it effortlessly cool -- and TBH, they look very good together.

These two have been locked in since making things official at Super Bowl LX ... and they’ve barely left each other’s side since, bouncing between Arizona, the UK, Colorado, and now back to Cali.