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Given a set of number, the GCF is a factor of every one of them. As a factor, it cannot be larger than them so the GCF is at most as large as the smallest of the number in the set.

The LCM of the same set is a multiple of each element in the set. The LCM must, therefore, be at least as great as the largest element in the set.


Thus if x is the smallest member of a set S and y is the largest, then

GCF <= x <= y <= LCM.


It can be proven that GCF = LCM if all the elements in the set are the same.

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7y ago

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