Problem

Source: Iranian TST 2019, third exam day 1, problem 2

Tags: Combinatorial Number Theory, number theory, combinatorics



Hesam chose $10$ distinct positive integers and he gave all pairwise $\gcd$'s and pairwise ${\text lcm}$'s (a total of $90$ numbers) to Masoud. Can Masoud always find the first $10$ numbers, just by knowing these $90$ numbers? Proposed by Morteza Saghafian