The $6740 when prorated is $3772. The credit given is the lower of tax liabilities on the taxable income. The method for computing taxable income varies between locations along with the tax rate.
For example: $10,000 in state A might be taxable income of $9500 with a 10% tax rate for $950 liability. State B taxes all $10,000 but at 5% for $500 liability. Your credit would be the lowest, $500. You can see where different variations will have different outcomes.
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