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The Lifetime Learning credit is a non-refundable credit. If you only have income of $10,838, then it is less than the standard deduction of $12,200 and you have no income tax liability which could be reduced by the Lifetime learning credit.
You should a tax liability for self-employment tax that the LLC cannot offset.
and the self-employment tax should be $1532 and as @MinhT1 noted, it can not be offset by the learning credit
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