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AMO 2027 Grades 9-11 SET 3 - Self-study Question 15

AMO · AMO 2027 Grades 9-11 SET 3 - Self-study

Question 15

Find the sum of positive integers $p,q,r$ given
$$\gcd(p,q)=45,\quad\gcd(q,r)=21,\quad\gcd(p,r)=3,$$
$$\operatorname{lcm}(p,q)=4725,$$
$$\operatorname{lcm}(q,r)=11025,\quad\operatorname{lcm}(p,r)=6615.$$

Enter one positive integer, without units.