This is a variation of the "Why do we have to know this?" debate that has plagued teachers and students as long as there have been teachers and students. The nasty truth is that there are a great many things that you encounter that will turn out to have little or no practical effect on your life. I find joy in problem solving, but you may not. Finding least common multiple answers sharpens your powers of deductive reasoning and that may turn out to be a useful tool or you. At the very least, you may one day have children who need help with their math homework.
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