MathDB

$\frac{1}{[a,b]} + \frac{1}{[b,c]} + \frac{1}{[c,d]} + \frac{1}{[d,e]}$

Source: Moldova TST 1999

August 7, 2023

number theory

Problem Statement

Let

a, b, c, d, e

(a < b < c < d < e)

be positive integers. FInd the greatest possible value of the expression

\frac{1}{[a,b]} + \frac{1}{[b,c]} + \frac{1}{[c,d]} + \frac{1}{[d,e]}

, where

[x,y]

denotes the least common multiple of

x{}

and

y{}