[ Decimal number system ] [ GCD and LCM. Mutual simplicity ]

Complete the number 523... with three digits so that the resulting six-digit number is divisible by 7, 8, and 9.

#
The obtained number must be divisible by $7 \cdot 8 \cdot 9=504.523000=1037 \cdot 504+352$. Since $504-352=152$, numbers divisible by 504 are 523152 and

$523152+504=523656$.

## Answer

523152 or 523656.