When you say, "I could care less" it means that you do have a level of caring about the subject at hand. When you say, "I couldn't care less" it means that you care so little about the subject that you lack the capacity to care less about it. Saying that you could care less simply doesn't make any sense if you're trying to state that you don't care about a specific subject. Thusly, when you're wanting to imply that you don't care about something, you need to utilize the couldn't version of the statement, as the could version is quite simply a silly thing to say.
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