Can two numbers have a GCF that is bigger than their LCM? Explain how you know?

The answer to this question would be: No, they can't

Greatest common factor biggest possible value is the number value itself. There is no factor that bigger than the number.

But the least common multiple smallest possible value is the number. There is no multiple that smaller than the number.

So it is not possible to have GCF bigger than LCM.