Personally, 1 credit card with high credit limit (3000-5000) should be enough.
or 2 combine to reach that amount.
So, if you have a LoC, paid off the in the order of amount. ie. 5500, 5500, 2300.
Cover as much as possible with your LoC, then pay interest only on LoC. and the rest of the money goes to the credit card with least amount.
Here is an example:
#1 5500
#2 5500
#3 2300
LoC 10000 (assume 8%)
Current situation:
Minimum credit card payment: 400
Minimum LoC payment: 0 ( since you haven't use )
My suggestion:
Use $10000 to pay #1, and $4500 to #2
After:
Minimum credit card payment: 99 (originally 400, saved 301)
Minimum loc payment: 70 (originally 0, extra 70)
Money saved: 231
Use your money saved, pay extra $231 to pay #2 (after minimum payment) and will pay off in 5 months.
After 5 months:
Credit card balance: #1 0, #2 0, #3 2200
Minimum credit card payment: 66
Minimum LoC payment: 70
Money available: 264
Pay everything you saved, extra $264 to #3 and will pay off in 8 months.
After 8 months, you will have only LoC left.
If you pay $400 to LoC (include interest), you can pay off in 25 months.
Total time needs to take: 3 years and 2 months.
If you don't take my approach, you will pay off all credit cards in 25 years.
Hope that helps.