Question 1189525
 the smallest positive multiple of {{{450}}} whose digits are all {{{zeroes}}} and {{{ones}}}?


We know  that it must be an {{{even}}} multiple of {{{450}}}. Otherwise the last two digits will be {{{50}}}.

first multiple is {{{900}}} 

what is the smallest {{{positive}}} multiple of {{{900}}} such that all the digits are {{{0}}}s or {{{1}}}s?

apply a  rule of multiples of{{{9}}}: 

the sum of the digits of a multiple of {{{9}}} is a multiple of {{{9}}} 

This rule goes both ways. If the sum of the digits is a multiple of {{{9}}}, the number is a multiple of {{{9}}}.

That makes {{{11111111100}}} our number.

check: {{{ 450*24691358= 11111111100}}}