In most cases, paying credit card balances will improve your credit score because it reduces your total debt. However, I would not close any of the paid off cards unless you have to close them for other reasons. It will help your score if you have borrowing capacity that you are not using. If you have a history of late payments with these cards, paying them off will not erase that history. But being paid off will help you of course, and as time passes, and the late payments are further and further in the past, they will affect your score less.
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