Why does Greg think that n can only have 2^2 because n^2 is 2^3 hence it “gets the job done”?

And why does 3^2 have to be so when n^2 is 3^3?

I don’t understand the logic. Saying n = 2^2 just because n^2 = 2^4 would be able to “get the job done” does not make sense. Same with the logic for the 3.

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the question ask for every integer in set S

thus, we can find the **LCM** of 24 and 108 because it will give us the **smallest number** that is divisible by both numbers.

LCM\{108,24\} = 216

Prime factorization of 216 = 2^3 \times 3^3

Now, according the question we need to find divisors of every integer n

But here 216 is the **LCM** of n^2

thus, to find n, n = \sqrt{216} \text{ or } \sqrt{2^3 \times 3^3}

Know we now that n is an integer and hence, we need a even number on it;s prime factor hence we add an additional 2 \text{ and } 3.

n = \sqrt{2^4 \times 3^4}

Solving the square root , n = 2^2 \times 3^2 = 36

Now, only 12 is a divisor of n !

I saw the video a long time ago, so I don’t remember the answer, but following the logic, shouldn’t 36 be also a divisor of n?