how can I file an extension for my LLC taxes

It depends on how your LLC is treated for tax purposes.  If you have a single member LLC (that hasn't elected S-Corp Status), the IRS considers it a "Disregarded Entity".  You report your income and expenses on Schedule C as part of your personal tax return.  When you file an extension  (Form 4868) for you personal return, you are filing an extension for your LLC.  If you have an LLC that has elected S-Corp status, then you file an extension (Form 7004) for Form 1120-S.  And if you have a multi-member LLC that doesn't have an S-Corp election, your LLC is taxed as a partnership and files Form 1065.  To file an extension you file Form 7004 for a 1065.