You don't have to file a tax return for an LLC with no income and no expenses, unless it is taxed as an S-Corp, in which case you have to file a Form 1120-S. If you have a single member LLC with no income and expenses, you only have to file a return if you are otherwise required. See the following IRS webpage to determine if you have to file a return:
Check if you need to file a tax return
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