1

Part of 1999 Moldova Team Selection Test

Problems(1)

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

Source: Moldova TST 1999

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]}

[x,y]

denotes the least common multiple of

x{}

y{}