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# Please help!

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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?

Apr 10, 2018

### Best Answer

#1
+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

### 3+0 Answers

#1
+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
+2

I get  99

9 + 9  =  18

99 / 18   =  5.5   Apr 10, 2018
#3
+1

Sorry, hectictar....I didn't see your answer when I posted....!!!   Apr 10, 2018