14.1.11 * Try to append 3 digits after $523 \cdots$ so that the resulting 6-digit number is divisible by $7$, $8$, and $9$.


Parse $7 \times 8 \times 9=504$. Since $524000=344(\bmod 504)$, then $524000-344=$ 523656 and $524000-(504+344)=523152$ are both divisible by $7,8,9$.