Form 1116 uses the lower of tax liabilities. Here is a link with how the credit is calculated. See here which includes this synopsis:
1) then a ratio is computed of foreign source income (line 1a) to gross income (line 2e) = line 2f
2) 2f is then multiplied by the amount on 3c = line 6
3) line 1a is reduced by line 6 to come up with net foreign income line 7
4) line 7 is divided by taxable income (line 18) to come up with a ratio line 19
5) your FTC is then line 19 multiplied by your tax (line 16) or if smaller the amount of your FTC
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