Can a franchise be purchased as an LLC?

Yes.  It is quite common for a franchise to be operated under a legal entity of some form other than a sole proprietorship. This could be a corporation, LLC, partnership or whatever works best for you.

It is common for a franchise company to require the main owners of the company to personally guarantee the performance of the company in relation to the franchise agreement, just as you'll probably have to personally guarantee the lease and other obligations of the business.

You should discuss the type of legal entity that is best for you with your legal and accounting advisors before making a final decision on how you want to proceed.