Question 1132855


Notice that the difference in each of those cases is {{{3}}}. ({{{7-4}}}, {{{8-5}}}, {{{9-6}}}) 

Ask yourself what would happen if you added {{{3}}} to this number? 

Well, when you divided the new number by {{{7}}}, you would get a remainder of {{{7}}}, which means {{{no}}} remainder. Same thing for {{{8}}} and {{{9}}}. 

So this new number is a common multiple of {{{7}}}, {{{8}}}, and {{{9}}}. And because you are looking for the {{{least}}}{{{ positive}}} integer, the new number must be {{{7*8*9=504}}}. 
Since we added {{{3}}} to the number, we have to subtract {{{3}}} to get the number you are looking for, {{{501}}}. 

check:

{{{501}}} divided by {{{7 = 71}}} remainder {{{4 }}}
{{{501 }}}divided by {{{8 = 62}}} remainder{{{ 5 }}}
{{{501}}} divided by {{{9 = 55}}} remainder {{{6}}}