KöMaL 2026 B5550

Is it possible to find positive integers $a$, $b$, $c$ satisfying $\mathop{\rm lcm}(a,b)+\mathop{\rm lcm}(a,c)+\mathop{\rm lcm}(b,c)=\mathop{\rm lcm}(a,b,c)?$ ($\mathop{\rm lcm}(x_1,x_2,\ldots,x_n)$ denotes the smallest common multiple of positive integers $x_1$, $x_2$, $\ldots$, $x_n$.)