Question 2
Positive integers $a,b,c,d$ satisfy
$$\gcd(a,b,c)=b,\qquad \gcd(b,c,d)=c,$$
$$\operatorname{lcm}(a,b,c)=60,\qquad \operatorname{lcm}(b,c,d)=600.$$
Find the smallest possible value of $a+b+c+d$.
$$\gcd(a,b,c)=b,\qquad \gcd(b,c,d)=c,$$
$$\operatorname{lcm}(a,b,c)=60,\qquad \operatorname{lcm}(b,c,d)=600.$$
Find the smallest possible value of $a+b+c+d$.