The proper idiom is spelled with the negative, as shown in the title. 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 wondering whether the writer intended to be witty or was just dumb. I have even seen some defend the positive (could care) form 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, negative, form is not an idiom, and the positive form carries opposite meaning, useful and useable on its own. Avoid misspelling the idiomatic phrase (e.g., I couldn’t care less) unless you wish your readers to view you as careless and ignorant.