Weakening of GCD: maximal common divisor (MCD)

Question

I'm dealing with integral domains and have come across the following weakening of the notion of a GCD (which I will write analogously as MCD): https://en.wikipedia.org/wiki/Maximal_common_divisor

Let $R$ be an integral domain and $A\subset R$. The following statements are formulated up to associatedness.

It's pretty obvious that

1. if the GCD of $A$ exists, it's also an, and the only, MCD of $A$.

I'm wondering if the converse is also true:

2. If there is exactly one MCD of $A$, it is the GCD of $A$.

Or is there a counterexample with, for instance, two divisibility chains of common divisors of $A$ starting from $1$ such that one of them has finite length (terminating in the MCD) while the other has infinite length? So in order to find a counterexample, $R$ must necessarily violate the ACCP, right?