Moab is the name of a place and a person. The person named Moab was a son of Lot and a brother of Ben-Ammi. After Lot and his two daughters were spared from the destruction of Sodom and Gomorrah, they fled to a cave in the hills above Zoar. Lot's two daughters conspired to preserve their line, by getting Lot drunk and having incestuous relations with him. A son, Moab, was born to the elder daughter, and became the ancestor of the Moabites. The younger daughter also bore a son named Ben-Ammi, who became the ancestor of the Ammonites (Genesis 19:30-38). Moab means "from my father."
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