# Prove that this process will stop

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

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