A $6$-digit number starting with $18$, $18ABCD$, is a multiple of $6$, $7$, $9$ and $10$. Find $\left (A +B + C+ D\right )$ for the smallest such number? 
Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples
The LCM of $6$, $7$, $9$ and $10$ is $2 \times 3^{2}\times 5 \times7= 630$.  $180 000=285 \times 630 + 450$,  ∴$$$$the$$$$ smallest number is $286 \times 630=180 180$,  Sum of the last 4 digits, $A + B + C+ D=9$. 