Question 934279
<pre>
It can't be a 4 digit number or larger because 1000/13 = 76.9 
and the largest possible sum of 4 digits is of 9999 which is only 36.

It can't be a 2-digit number because 10x13=130 a 3 digit number.

So it must be 3-digit number:

{{{100h+10t+u=13(h+t+u)}}}
{{{100h+10t+u=13h+13t+13u}}}
{{{87h=3t+12u}}}
{{{29h=t+4u}}}
{{{t=29h-4u}}}

{{{0<t=29h-4u<=9}}}

h must be 1 because if it were 2 or greater, 
u would have to be greater than 9.

{{{29-4u<10
{{{4u>19}}}
{{{u>4.75}}} 

So u  is 5,6, or 7.  It can't be 8 for that would make t negative

{{{t=29-4u}}}
If u=5, t=9, and the number ia 195

If u=6, t=5, and the number is 156  

If u=7, t=1, and the number is 117
 
Answer: The smallest is 117.

Edwin</pre>