I have three credit cards with balances on them, which should I pay off first?

From FinancialPlanning

The Fastest Way

Pay off the card with the highest rate first, then move on to the next-highest rate, and so on until you've paid off all of your debts. This approach will result in the lowest amount of interest charges, so is the quickest way to being debt-free. This is true regardless of the amount of debt at each interest rate.

For example if you have three credit card balances that you aren't able to pay in full:

$200 at 8% interest
$2,000 at 14% interest
$500 at 10% interest

the fastest repayment plan would be to pay off the 14%-rate balance first, then the 10%-rate balance, and then the last $200 (while paying at least the minimum payment each month on all of them). If you pay off the $200 balance first, you'll just have an additional $200 on the 14% card, when you instead could have been paying 8% interest on that $200.

Paying off the Smallest Balances First

A point sometimes made on MIFP when this question comes up is that there's a psychological aspect to getting out of debt. Some people will get frustrated at having a bunch of credit card balances sitting there, while chipping away at just one of them. So frustrated that they give up and let the balances creep back up again. For this reason, some people might choose to pay off smaller balances first, simply for the satisfaction of paying something off. You still end up paying more interest but if the alternative is not paying off the debt, that may be the lesser of two evils.