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The greatest common multiple of any set of integers is infinite.

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Q: What is the gcm of 45 and 21?
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What is the GCM of 25 and 45?

The GCF is 5. The LCM is 225. The GCM is infinite.


What is the gcm of 10 and 21?

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What is the GCM of 7 and 13?

There can be no GCM (Greatest Common Multiple). Suppose a GCM exists and suppose it is x. That is, x is the GCM of 7 and 13, then 2x is a multiple of both 7 and 13 and is greater than x. This contradicts the statement that x is the GCM. So x cannot be the GCM.