How would paying off the lowest outstanding balance credit card first be beneficial over paying off the one with the highest interest rate?

This is referred to as the snowball method. By starting with the smallest outstanding balance, you will pay off the amount faster, resulting in a feeling of gratification that will carry you on to the next smallest outstanding balance. If you were to start with the loan that has the highest interest rate, it would be more difficult to maintain this momentum because it would take longer to pay it off in full.