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We have a written sequence $a_1, a_2,.., a_n$. We can choose any two numbers $a, b$ from this sequence so $a∤b, b∤a$ and change them with GCD$(a,b)$ and LCM$(a,b)$. Prove that this process is not endless.
P.S.
GCD - Greatest Commmon Divisor
LCM - Least Common Multiple

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  • $\begingroup$ The process stops when you can no longer find $a$ and $b$ such that neither is a multiple of the other? $\endgroup$ – Fabio Somenzi Jan 5 '18 at 17:38
  • $\begingroup$ Do you see that $\gcd(a,b) \mid \operatorname{lcm}(a,b)$? $\endgroup$ – Fabio Somenzi Jan 5 '18 at 17:44
  • $\begingroup$ Thank you very much!!! What a damn fool I am... $\endgroup$ – Peter338 Jan 5 '18 at 17:53

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