It's "I couldn't care less", as in, it wouldn't be possible for me to care any less if I tried, because I care so little.
If you say "I could care less" you're logically implying that you do care
It's "I couldn't care less", as in, it wouldn't be possible for me to care any less if I tried, because I care so little.
If you say "I could care less" you're logically implying that you do care