As shown in the title, the proper phrase indicating complete uninterest is spelled with the negative. I’m dismayed by how many writers can’t care enough to include the necessary negative, writing nonsense like I could care less, which leaves readers uncertain whether the writers tried to be witty or were just dumb. I have even seen some usage writers defend the positive form (could care) on the grounds that the negative is an idiom and can thus be understood even when incorrectly written as a positive. The problem with this argument is that, while idiomatic, the correct expression is not an idiom, and the positive form carries useful and usable meaning on its own. Avoid misspelling the idiomatic phrase couldn’t care unless you want your readers to view you as careless and ignorant.