a) Do there exist positive integers $a$ and $d$ such that $[a, a+d] = [a, a+2d]$? b) Do there exist positive integers $a$ and $d$ such that $[a, a+d] = [a, a+4d]$? Here $[a, b]$ denotes the least common multiple of integers $a, b$.
Source: Kyiv City MO 2022 Round 2, Problem 7.1
Tags: number theory, LCM
a) Do there exist positive integers $a$ and $d$ such that $[a, a+d] = [a, a+2d]$? b) Do there exist positive integers $a$ and $d$ such that $[a, a+d] = [a, a+4d]$? Here $[a, b]$ denotes the least common multiple of integers $a, b$.