To find the smallest number $n$ we need a number with
the smallest possible number of significant digits. Since
the number $n$ has to end with $56$ and its digit sum
has to be $56$, it will be better for us to
start with $n=9999956$, however this number won't satisfy
the second requirement, so we shall modify $n$ to meet all
the requirements. Notice that $7\cdot 2^3=56$, so $n$ has to
be divisible both by $2^3$ and $7$. Now $n$ is to be
divisible by $2^3=8$ if its last digits are divisible by $8$,
thus we modify as follow: $n=19999856$. Nevertheless this
number won't be divisible by $7$, to fix it we need to
modify $n$ in such a way that it will remain the least number
possible. The price of modifying $n$ is adding $1$ to the
first digit while reducing $1$ from other most significant
digit, so we check $n=28999856$, but this number is not
divisible by $7$. So we can reduce the instead of decreasing
one from the second digit we decrease one from the third
digit, we get $n=29899856$ this number is divisible by
$7$ and by $8$ and therefore meets all the requirements.