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Latter-day Saints abide the law of the land in which they live; honorably answering a call when conscripted for military service is part of this belief. Volunteer military service is also respected as a way of serving one's country. Latter-day Saints should live in accordance with the revealed will of the Lord and according to their own conscience.
Latter-day Saints in the military do not need to feel torn between their country and their God. In the Church, βwe believe in being subject to kings, presidents, rulers, and magistrates, in obeying, honoring, and sustaining the lawβ (Articles of Faith 1:12). Military service shows dedication to this principle.
(From https://www.lds.org/topics/war)
This happened in WW2. There's even a movie based on a true account about this ("Saints and Soldiers"). War is awful, but Mormons accept this reality where they do not have the power to avoid it.
Further reading: http://www.mormonnewsroom.org/article/military-service