+0

+2
398
3
+4228

A lucky integer is a positive integer which is divisible by the sum of its digits. What is the least positive multiple of 9 that is not a lucky integer?

Apr 10, 2018

#1
+7616
+1

The sum of the digits for each of the first ten multiples of 9  is  9 .

So the first 10 positive multiples of 9 must be lucky integers.

 9 * 1  =  9 and 9/9  =  1 9 * 2  =  18 and 18/(1+8)  =  2 9 * 3  =  27 and 27/(2+7)  =  3

etc.

But....

9 * 11  =  99     and     99/( 9 + 9 )  =  5.5

So

99  is the least positive multiple of  9  that is not a lucky integer.

Apr 10, 2018

#1
+7616
+1

The sum of the digits for each of the first ten multiples of 9  is  9 .

So the first 10 positive multiples of 9 must be lucky integers.

 9 * 1  =  9 and 9/9  =  1 9 * 2  =  18 and 18/(1+8)  =  2 9 * 3  =  27 and 27/(2+7)  =  3

etc.

But....

9 * 11  =  99     and     99/( 9 + 9 )  =  5.5

So

99  is the least positive multiple of  9  that is not a lucky integer.

hectictar Apr 10, 2018
#2
+100588
+2

I get  99

9 + 9  =  18

99 / 18   =  5.5

Apr 10, 2018
#3
+100588
+1