MathDB

3

Part of 2021 Lotfi Zadeh Olympiad

Problems(1)

find min [lcm(a,b)+lcm(b,c)+lcm(c,a)]/[gcd(a,b)+gcd(b,c)+gcd(c,a)]

Source: Lotfi Zadeh Olympiad 2021, Problem 3

12/28/2021
Find the least possible value for the fraction lcm(a,b)+lcm(b,c)+lcm(c,a)gcd(a,b)+gcd(b,c)+gcd(c,a)\frac{lcm(a,b)+lcm(b,c)+lcm(c,a)}{gcd(a,b)+gcd(b,c)+gcd(c,a)} over all distinct positive integers a,b,ca, b, c. By lcm(x,y)lcm(x, y) we mean the least common multiple of x,yx, y and by gcd(x,y)gcd(x, y) we mean the greatest common divisor of x,yx, y.
number theoryLCMGCDLotfi Zadeh MO