Mew was distributed at an event once, but that is long over and sadly if you want a mew in leafgreen now, you'll need help from other games or you could use cheat codes.
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Some people say to nickname your starter Pokemon "Mew" and it will play as mew for the rest of the game but I never tested it...
mewtow zapdos moltres articuno mew entei raikou suicune
mew-two is lvl. 70 in cerulian cave. make sure you save a masterball for him
Almost every pokemon in Leaf Green can be found up your ass, except for Mew nad Mewtwo who are most commonly found below your nutsack..
i hate pokemon!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1