If $\gcd(a,b)=d_1$ and $\gcd(b,c)=d_2$, what can we say about $\gcd(a,c)$

Question

If $\gcd(a,b)=d_1$ and $\gcd(b,c)=d_2$. Here $d_1$ and $d_2$ are not $1$. In addition we have $\gcd(d_1,d_2)=1$. Can we say $\gcd(a,c)=1$ ? The question seems easy but I am not able to see whether it is true or not? If it is true please help me to prove this! Thank you!