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

#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.

hectictar Apr 10, 2018

#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