VTMO 2026 - Grade 6 - Semifinal - SET 4 - Self-study Question 16

Natural numbers $a,b,c$ satisfy $\gcd(a,b)=30$, $\operatorname{lcm}(a,b)=180$, $\gcd(a,b,c)=15$ and $\operatorname{lcm}(a,b,c)=900$. Find the smallest possible value of $a+b+c$.