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Iran combinatorial number thoery

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

April 25, 2019
Combinatorial Number Theorynumber theorycombinatorics

Problem Statement

Hesam chose 1010 distinct positive integers and he gave all pairwise gcd⁡\gcd's and pairwise lcm{\text lcm}'s (a total of 9090 numbers) to Masoud. Can Masoud always find the first 1010 numbers, just by knowing these 9090 numbers?
Proposed by Morteza Saghafian
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