MathDB

{gcd(a,b),gcd(b,c),gcd(c,a), lcm(a,b), lcm(b,c), lcm(c, a)}= {2, 3, 5, 30, 60}

Source: Switzerland - 2013 Swiss MO Final Round p1

December 30, 2022

number theorygreatest common divisorleast common multipleLCMGCD

Problem Statement

Find all triples

(a, b, c)

of natural numbers such that the sets

\{ gcd (a, b), gcd(b, c), gcd(c, a), lcm (a, b), lcm (b, c), lcm (c, a)\}

and

\{2, 3, 5, 30, 60\}

are the same.
Remark: For example, the sets

\{1, 2013\}

and

\{1, 1, 2013\}

are equal.