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Is the positive integer \(x\) prime?

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Re: Is the positive integer \(x\) prime?

by Ian Stewart » Tue Jun 08, 2021 4:22 am

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I assume the question means to tell us y is some positive integer.

If x and y are positive integers, then when we multiply their LCM and their GCD, we always get their product xy. So if their GCD is 1, that automatically means their LCM is xy, and if their LCM is xy, that automatically means their GCD is 1.

So the two statements say exactly the same thing, and the answer can only be D or E. And the answer is E, because the GCD of two numbers can certainly be 1 when neither number is prime. For example, we might have x = 4 and y = 25, and x might not be prime, or we could have x = 2 and y = 25, and x might be prime.
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