MathDB

The numbers

1,2,3,4,\ldots , 39

are written on a blackboard. In one step we are allowed to choose two numbers

a

and

b

on the blackboard such that

a

divides

b

, and replace

a

and

b

by the single number

\tfrac{b}{a}

. This process is continued till no number on the board divides any other number. Let

S

be the set of numbers which is left on the board at the end. What is the smallest possible value of

|S|

?
Proposed by B.J. Venkatachala

Problem Statement