וַיִּבְחַר־ל֣וֹ ל֗וֹט אֵ֚ת כָּל־כִּכַּ֣ר הַיַּרְדֵּ֔ן וַיִּסַּ֥ע ל֖וֹט מִקֶּ֑דֶם וַיִּפָּ֣רְד֔וּ אִ֖ישׁ מֵעַ֥ל אָחִֽיו׃
그러므로 롯이 요단 온 들을 택하고 동으로 옮기니 그들이 서로 떠난지라
Sforno on Genesis
ויבחר לו לוט, he selected as much area as he himself with his shepherds would manage to control as their grazing land. In this section of the earth Avram and his shepherds would not be allowed to graze.
Radak on Genesis
ויבחר לו לוט את כל ככר הירדן, the reference is to one area within the Jordan valley, the use of the word כל here meaning that all the areas within that region were equally good as grazing land for his flocks.