Question 75
Determine all quadruples $\left(a, b, c, d\right)$ of non-negative integers, with $a, b, c$ strictly positive, such that
$$
\begin{aligned}
& \operatorname{lcm}(b, c)=a+d \\
& \operatorname{lcm}(c, a)=b+d \\
& \operatorname{lcm}(a, b)=c+d
\end{aligned}
$$
$$
\begin{aligned}
& \operatorname{lcm}(b, c)=a+d \\
& \operatorname{lcm}(c, a)=b+d \\
& \operatorname{lcm}(a, b)=c+d
\end{aligned}
$$