This one is mainly spoken, but still appalling. The phrase should be “I couldn’t care less”. This makes perfect sense as it states that it would not be possible for you to care less about something, and so it must be completely at the bottom of your mental totem-pole.
However, how many times have you heard “I could care less”. People will even vehemently defend this as being correct! What this means is that it IS possible for something to be less significant to you than whatever it is you are discussing. So, this ascribes importance, where the whole point is to say that whatever it is has NO importance.