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LCM genius problem from our favorite author

Source: Kyiv City MO 2022 Round 2, Problem 8.1

January 30, 2022
number theoryleast common multiple

Problem Statement

Find all triples (a,b,c)(a, b, c) of positive integers for which a+[a,b]=b+[b,c]=c+[c,a]a + [a, b] = b + [b, c] = c + [c, a].
Here [a,b][a, b] denotes the least common multiple of integers a,ba, b.
(Proposed by Mykhailo Shtandenko)
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