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I was in a similar situation recently. I first paid against any that were over 89% utilization to get them out of maxed out. I then started paying lowest to highest balance.
Reducing the maxed out ones gave me the biggest jump in score, followed by zero balances on a few others.
Hope this helps.
I myself would probably pay off across all cards, in weighted amounts. The reasoning would be, to lower both the overall and individual util across the board, as I do recall there being some word about keeping util under around 90% to avoid getting the "maxed out card" designation.
Based on your numbers, I ran it through a quick excel analysis (I get bored at work =X):
Current Bal | Limit | Current Utilization | New Balance | Payment Needed |
$ 11,680.00 | $ 12,000.00 | 97% | $ 8,400.00 | $ 3,280.00 |
$ 2,800.00 | $ 3,000.00 | 93% | $ 2,100.00 | $ 700.00 |
$ 4,400.00 | $ 4,500.00 | 98% | $ 3,150.00 | $ 1,250.00 |
$ 2,700.00 | $ 3,000.00 | 90% | $ 2,100.00 | $ 600.00 |
$ 580.00 | $ 800.00 | 73% | $ 560.00 | $ 20.00 |
$ 2,900.00 | $ 3,000.00 | 97% | $ 2,100.00 | $ 800.00 |
$ 1,100.00 | $ 1,600.00 | 69% | $ 1,100.00 | $ 0.00 |
$ 1,800.00 | $ 2,000.00 | 90% | $ 1,400.00 | $ 400.00 |
TOTAL PAYMENT | $ 7,050.00 |
(very simplified analysis, I think SusieQ's suggestion might be better, first and foremost bring down the "maxed out" balances down under 90%, then zero out the lower balances then whatever may or may not be left over can be used to paydown the remaining higher balances)
[Edited for some math errors]