Your personal credit will affect your ability to purchase a home. In nearly all cases the lender will require you to personally guarantee the loan to an LLC and your credit will therefore be a deciding factor. That being said -- credit is only one factor lenders consider and it is less important as the loan to value ratio decreases.
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An LLC is a legal entity which can acquire and own property. Therefore, the answer to your question is yes, an LLC can purchase a home. That being said, unless your LLC has sufficient assets and/or credit history, a personal guaranty from you will be necessary. The lender will seek to minimize the risk of their loan as much as possible.
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