Generally, taxes can be due when you buy (sales tax), own (property tax or franchise tax), or earn (income tax).
Montana is one of a handful of states that doesn’t levy a sales tax. Because you pay sales tax on a vehicle where you register it, not where you buy it, registering your vehicle in Montana can save you hundreds or thousands of dollars in sales tax.
Montana doesn’t levy a property tax on vehicles, and it doesn’t levy a franchise tax (a type of tax imposed by some states for owning a corporation or LLC within that state) at all.
Income tax would be due to Montana and the US government if your LLC were to earn income. However, if your LLC just exists to own a vehicle (that will be worth a bit less when you sell it), it’s unlikely that your LLC will generate any income to be taxed.