VTMO 2026 - Grade 7 - Semifinal - SET 8 - Self-study Question 16

Let $a,b,c,d$ be distinct natural numbers such that $\gcd(a,b,c)=a$, $\gcd(b,c,d)=b$, $\operatorname{lcm}(a,b,c)=45$ and $\operatorname{lcm}(b,c,d)=450$. Find the smallest possible value of $d$.