I believe the best way to answer this question is to give LDS interpretation on all of Isaiah chapters 40-48. There are many verses that discuss there being only one God. I will start by discussing the purpose of these verses being written. Isaiah is speaking to many people who are looking to "Other gods" to be saved. People are trying to create their own Gods, and overall turning from their God. People often interpret these verses as there is only one God in exhistance, but LDS interpret them as there is only one God who we can turn to to be saved. I will give an example.
Isaiah 43:10 Ye are my witnesses, saith the LORD, and my servant whom I have chosen: that ye may know and believe me, and understand that I am he: before me there was no God formed, neither shall there be after me. 11 I, even I, am the LORD; and beside me there is no saviour. (KJV)
LDS interpretation is based on the subject being reffered to, or in other words the idea of going to other gods to be saved. It is specified in verse 11 that there is no savior. In other words it is interpreted by LDS that we only have one God we can turn to to be saved. One God that is our God.
Some verses that add a better definition to the phrase "No God beside me" are
Isaiah 47:8 Therefore hear now this, thou that art given to pleasures, that dwellest carelessly, that sayest in thine heart, I am, and none else beside me; I shall not sit as a widow, neither shall I know the loss of children:
10 For thou hast trusted in thy wickedness: thou hast said, None seeth me. Thy wisdom and thy knowledge, it hath perverted thee; and thou hast said in thine heart, I am, and none else beside me.
Based on these verses it adds a second meaning to the phrase. When used here only a few chapters later it isn't meant the mean the only one in existence, but the greatest, or most powerful. "none else beside me" can be taken to mean that none can overthrow, or none can challenge.
Due to shortness of time I cannot give a long answer but I may add to this one in a few days. I hope this at least helps put that interpretation in context.
For a more detailed answer this site has good information on the subject: