An LLC is a legal entity, not a tax identity. If you are the sole owner and never requested to be a corporation, it is part of your tax return, on sch C. Just file your personal extension, the business is part of it.
Otherwise, the tax deadline was Mar 15.
Be sure to make any payments by April 15. You can make Payments online safely. Remember your Self-employment tax is included in the amount due. Only the paperwork is extended. See:
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