Prove that this process will stop

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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