<s>[INST] Minimum Possible Number How to find the minimum possible number of length N ,which is simultaneously divisible by the single digit prime number like 2,3,5,7  ?like of length 5 minimum possible number is 10080. 
 [/INST] As the lcm of $2,3,5,7$ is $210,$ we need to find the minimum multiple in $N$ digits.
So, $N$ must be $\ge 3$ to admit solution.
The minimum natural number with $N$ digits is $M=100\cdots00$ with $(N-1)$ zeros.
So, if $D=\lfloor\frac M {210}\rfloor,$ the answer will be $210(D+1)$
For example if $N=4,D=\lfloor\frac {1000} {210}\rfloor=4,$ the answer will be $210(4+1)=1050$
As pointed out by Thomas in his comment,
we can use Carmichael Function, $\lambda(21)=lcm(\lambda(3), \lambda(7))=lcm(2,6)=6$
So, $10^6\equiv1\pmod {21}\implies 10^{6m}\equiv1\pmod {21}$
$\implies 10^{6m+1}\equiv{10}\pmod {210},$ the minimum number with length $(6m+1+1)=6m+2,$ will be $10^{6m+1}+(210-10)$
$\implies 10^{6m+2}\equiv{100}\pmod {210},$ the minimum number with length $6m+3,$ will be $10^{6m+1}+(210-100)$
and so on.
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