The LDS interpret that scripture the same way we interpret these Book of Mormon Scriptures:
3 Nephi 11:27
27 And after this manner shall ye baptize in my name; for behold,
verily I say unto you, that the Father, and the Son, and the Holy
Ghost are one; and I am in the Father, and the Father in me, and the
Father and I are one.
Mosiah 15:4
4 And they are one God, yea, the very Eternal Father of heaven and of
earth.
3 Nephi 20:35
35 The Father hath made bare his holy arm in the eyes of all the
nations; and all the ends of the earth shall see the salvation of the
Father; and the Father and I are one.
3 Nephi 11:36
36 And thus will the Father bear record of me, and the Holy Ghost will
bear record unto him of the Father and me; for the Father, and I, and
the Holy Ghost are one.
Mormon 7:7
7 And he hath brought to pass the redemption of the world, whereby he
that is found guiltless before him at the judgment day hath it given
unto him to dwell in the presence of God in his kingdom, to sing
ceaseless praises with the choirs above, unto the Father, and unto the
Son, and unto the Holy Ghost, which are one God, in a state of
happiness which hath no end.
The Father sent His Son to help us to know, love, and obey our Father in Heaven. God the Father, Jesus Christ, and the Holy Ghost are indeed separate and distinct beings, but they are perfectly united in purpose; to bring to pass the immortality and eternal life of man.
Christ said in John 6:38:
38 For I came down from heaven, not to do mine own will, but the will
of him that sent me.
In all that Jesus came to say and do, including and especially in His atoning suffering and sacrifice, He was showing us who and what God our Eternal Father is like, how completely devoted He is to His children in every age and nation. In word and in deed Jesus was trying to reveal and make personal to us the true nature of His Father, our Father in Heaven.1
By seeing how the Father is, we can learn how to experience pure joy. That is why Christ said that if you have seen him, you have seen the Father, because Christ lived a perfect life, he showed us what the Father was like, and how we could have joy.
3 Nephi 28:10
10 And for this cause ye shall have fulness of joy; and ye shall sit
down in the kingdom of my Father; yea, your joy shall be full, even as
the Father hath given me fulness of joy; and ye shall be even as I am, and I am even as the Father; and the Father and I are one;
Note in the above scripture, "...ye shall be even as I am, and I am even as the Father, and the Father and I are one."
Christ was speaking to three of his disciples when he spoke these words, he told them that they would be one with Him and the Father.
This was a sure promise that they would be Exalted, like Christ, and the Father. If we choose to live the life Christ showed us to live, the life he showed us was like unto what the Father would live, then we too can be Exalted, we too can be one with the Father and have a fulness of joy.
1 Jeffery R Holland, He That Hath Seen Me Hath Seen The Father, Ensign, 2003
