Question 982672


Let &nbsp;<B>x</B>&nbsp; be the unknown number.

Then &nbsp;x-10&nbsp; is divisible by &nbsp;16, &nbsp;24, &nbsp;30 and &nbsp;36, according to the condition.


It implies that &nbsp;x-10&nbsp; is divisible by &nbsp;{{{2^4}}}, &nbsp;{{{5}}}&nbsp; and &nbsp;{{{9}}}.

Hence, &nbsp;x-10&nbsp; is divisible by &nbsp;16*5*9 = 720. 


The greatest &nbsp;5-digits number divided by &nbsp;720&nbsp; is &nbsp;99360 &nbsp;(it is easy to check).

It means that &nbsp;x-10 = 99360.

Hence, &nbsp;x = 99370.