The book "The Rise of Christianity" by Rodney Stark was an interesting discussion of the rapid growth of the LDS.

The main point was that the LDS like most religions, propagated via relatives and friends. People tend to "convert" when a preponderance of their friends and relatives have converted. It becomes increasingly uncomfortable to resist.

I suspect that atheism is benefiting from this syndrome at the moment.

Missionary work, including LDS, has a phenomenally low success rate. I don't recall it, but from memory a missionary might convert 1-2 people per year based on cold calls. I suspect that missionary work is done, not so much to get converts, as to reinforce the group identity of the missionaries.