Expert: Surajit Basu - 5/15/2008

Question
My son gave me this puzzle to do help.

using the numbers 0 to 9 what is the lowest integer that contains each of the numbers once only and can be divided by 2 though to 16

Answer
My son gave me this puzzle to do help.

using the numbers 0 to 9 what is the lowest integer that contains each of the numbers once only and can be divided by 2 though to 16


can be divided by 2 though to 16?
So, let's find the LCM of 2 to 16...

# Needs an extra factor of   because
2    2   
3    3   
4    2    2 is already there
5    5   
6    1    2 and 3 are there
7    7   
8    2    4 is there
9    3    3 is there
10    1    2 and 5 are there
11    11   
12    1    3 and 4 are there
13    13   
14    1    2 and 7 are there
15    1    3 and 5 are there
16    2    8 is there

So the LCM is 720,720.

So, the number we need has to be divisible by 720,720.

using the numbers 0 to 9 what is the lowest integer that contains each of the numbers once only and can be divided by 720,720

the required number has to end in a 0.

The min number is  1,234,567,890  ( has to have 10 digits)
So, 720,720 needs to be multiplied by at least ...  1,713

i am stuck after this...