If your LLC is a single owner (member), then you default to being self employed and you can use TurboTax Self-Employed. If you have a multi-member or elected S-corp status, then you can't do your business extension or taxes with the online editions of TurboTax.
Instead, you'll need the TurboTax Business which is desktop software. You can find it HERE. You can file your business extension in this software. With a separate business entity, you'll need to file your personal taxes after your business and enter the forms you receive from the business return (schedule K-1 and W-2 if applicable).
