# Lowest divisible number in number string

A number is arranged in a pattern like: 12345678910111213141516...

What is the lowest value of that pattern divisible by 72?

They are single numbers, not seperate (i.e. first in sequence is 1, second is 12, third, 123 etc)

• To be divisible by 72, it is necessary and sufficient for the number to be divisible by both 8 and 9. Do you know any way to tell if a number is divisible by 8 or by 9? – MJD Nov 26 '14 at 16:29

The first such numbers are $a_{36}$, $a_{44}$, $a_{144}$, $a_{152}$, $a_{216}$, ... So the lowest is $123\ldots343536$.