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From a least common multiple, you can show that every number below it is not a common multiple of the two numbers. However, there are an infinite number of multiples above the LCM that the two share, so you cannot label any of them as the "greatest common multiple." Easier way to think of it would be to take a supposed GCM and double it. The resulting number is now the GCM. Double it again, and you get a new GCM. This continues onto infinity.

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Q: Why dont you have a greatest common multiple?
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