The LDS send missionaries out because Heavenly Father has said to teach others about Him.
Matt 24: 13-14
13. But he that shall endure unto the end, the same shall be saved.
14. And this gospel of the kingdom shall be preached in all the world for a witness unto all nations; and then shall the end come.
Mark 16: 15-16
15. And he said unto them, Go ye into all the world, and preach the gospel to every creature.
16. He that believeth and is baptized shall be saved; but he that believeth not shall be damned.
And I think this one says it best:
1 Cor. 9: 16
16 For though I preach the gospel, I have nothing to glory of: for necessity is laid upon me; yea, woe is unto me, if I preach not the gospel!
There you go--question answered.