gcd and lcm - Help in proving the necessity part (If D is an integral domain, if $d_1=$gcd(a,b), then ..)

In an integral domain D, if $d_1$=gcd(a,b), then $d_2$=gcd(a,b) if and only if $d_1$ and $d_2$ are associates.

Attempt: Since $d_1$=gcd(a,b) then $d_1|a$ and $d_1|b$ which implies that $a=d_1c$ and $b=d_2e$ for $c,e \in D$. Likewise, if $d_2$=gcd(a,b), then $d_2|a$ and $d_2|b$ which implies that $a=d_1x$ and $b=d_2y$ for $x,y \in D$.

And from this, I don't know any trick to show that $d_1=ud_2$ where $u$ is a unit.

Any suggestions?