For all positive integers, If $a | b, b | c$ and $c |a$ then we must have $a = b = c$

Question

I have a hard time understanding why this statement is true, I have used many examples and it holds true if $a, b$ and $c$ are the same integer. Could someone help me understand why?

Answer 1

Note that $$a|b \implies a \le b$$ $$b|c \implies b \le c$$ $$c|a \implies c \le a$$ As $a,b,c$ are positive integers. So we have that $a \le b \le c \le a$. So we have $a=b=c$.