Life After Each Kill (LAEK) is an affix found on items (weapons and armor) in Diablo 3. The affix does what it sounds like; grants X amount of life (hit points) for each monster killed, whether a normal "white" enemy, an Elite, or even an Act Boss.
LAEK is a helpful affix to keep a health bulb topped off during regular play, but trash mobs are not very dangerous in Diablo 3. The danger in the game comes from Boss battles, and in those LAEK is of little use, since it doesn't heal during a battle with one or a few tougher enemies.
As a result, Life Steal and Life on Hit are much more useful and popular item modifiers.
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