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The LCM for any pair of natural numbers can be as big as their product.

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No, it cannot be smaller than the largest of the set of numbers.

The LCM can be any positive integer.

Not normally

It's never less than the largest number.

No.

Q: Is the LCM of a pair of numbers ever less than both numbers?

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No, it's never greater than the smallest number.

A square number

Because there are many examples where that isn't so. The GCF of 36 and 24 is 12. The GCF of 151 and 149 is 1.

I can't give you an example of when that happens because that doesn't ever happen. The GCF of a pair of numbers can't be larger than the smaller number.

False

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No.

No.

No.

No.

No. The LCM of 4 and 6 is 12.

The LCM is never less than the greatest number in the set. The LCM of 4 and 9 is 36.

No. At most, it can be equal to the smaller number.

A number can't have a factor greater than itself, so the GCF of a pair of numbers can't ever be greater than the smaller number. The GCF of 9 and 18 is 9.

No, it's never greater than the smallest number.

31

Not at all. For example: gcf(101, 102) = 1 gcf(40, 80) = 40

No, it's never greater than the smallest number.