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720
but so much more than credit score go into it.
It really depends what which card and which bank its from.
CreditAddict is right, there are so many variables that its hard to pick a specific number.
I would say 685 at the lowest if you have good income, low debt and a long credit history. If you don't have those things, you need to be 700+, and even then there is always a chance for denial.