What is the smallest positive integer that is divisible by $2$ and $3$ that consists entirely of $2$s and $3$s, and has at least one of each?
I was wondering if there a formula or steps to approach this problem? I did it directly starting with $23, 32, 232,233,223$,… until I got what I assume is the smallest integer.
$3,222$ is divisible by both $2$ and $3$.
Best Answer
Isn't $2232$ smaller and divisible by both?
Method. To be even it has to end in $2$. Then it needs three of them for the digit sum to be divisible by $3$. Then put the $3$ as far to the right as possible.