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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?

tertre  Apr 10, 2018

Best Answer 

 #1
avatar+6943 
+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
Sort: 

3+0 Answers

 #1
avatar+6943 
+1
Best Answer

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
avatar+85757 
+2

I get  99

 

9 + 9  =  18

 

99 / 18   =  5.5

 

 

cool cool cool

CPhill  Apr 10, 2018
 #3
avatar+85757 
+1

Sorry, hectictar....I didn't see your answer when I posted....!!!

 

 

cool cool cool

CPhill  Apr 10, 2018

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