Operating an LLC in three separate states
You can absolutely form an LLC in one state and then operate it in multiple states. Better yet, since you are doing business in multiple states, consider forming your company in one of the business havens: Wyoming, Delaware or Nevada.
After the LLC is formed, all you need to do is apply for authority to do business in every other state where you intend to operate your new company. This process is also sometimes called "forming a foreign entity," because your Utah corporation is "foreign" to Texas, for example. This is a rather straightforward process that simply registers your company with the states where you want to do business.