I had a strange debate about debt...

Can anyone help me solve this conundrum?
I was having a debate with a friend over the subject of clearing credit card debts, when one has several credit cards, each with a different
interest rate.
His approach to clearing overall debt as quickly as possible is to pay off the smallest debt first.
I qusetioned this approach. I put it to him that is makes more sense to pay down the debt with the highest interest rate first, regardles of whether it's the biggest or the smallest of the debts.
He is adamant that his approach is best for paying off the overall debt fastest. I do not see any logic in his approach.
Who has the better approach, him or me?
TIA!
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On Sun, 15 Nov 2015 06:21:17 +0000, Pass me the gentle persuader wrote:

I can see a kinda logic in his approach - in that he's reducing the sources of debt faster, so reducing the perception of debt. Except what really matters is the total, not the number of sources.
But, if you owe £10k at 10% and £1k at 5%, of course it makes sense to pay £1k off the bigger debt first.
£10k at 10% + £1k at 5% = £11k at 9.55% average. £9k at 10% + £1k at 5% = £10k at 9.5% average. £10k at 10% = £10k at 10% average...
Pay nothing else off over the year, that's a £50 reduction in the interest payable.
In a way, his way could be even more actively counterproductive. He's closed off the 5% source, so can't look into transferring any balance from the 10% source to it.
If he could pay £1k off and transfer £4k to the 5% source... £5k at 10% + £5k at 5% = £10k at 7.5% average.
£250 reduction over the year.
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Thank you; you have confirmed that my logic is sound. I'm not sure why my friend cannont grasp this too. Perhaps I'll suggest to him that he reconsiders his views after seeking the opinion of a couple of qualified financial experts. To me it seems just common sense though.
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This answer is corrupted by the 30 days free credit that you get on future purchase on a debt free credit card, which you lose if you already have an ongoing debt on that card.
By paying off one of you cards in full, rather than running them all with a smaller balance owing, you will at lease get the 30 days free credit on some of your purchases.
tim
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