Can you solve this question?

Question

A pirate has a wooden chest full of gold coins. If the coins are equally divided among 10 pirates, 9 coins are left in the chest. If they are equally divided among 9 pirates, 8 are left in the chest and if they are equally divided among 8 pirates, 7 are left in the chest. What is the least possible number of coins in the chest? One more thing, there are at least 500 coins.

Answer 1

if the number of coins is divided by 10 and there is a remainder of 1, this means that the number of coins is 1 less than a multiple of 10

similarly, for the same reasoning, the number of coins is 1 less than a multiple of 9 and 1 less than a multiple of 8

find the LCM of 10, 9, and 8

8=2*2*2

9=3*3

10=2*5

LCM=2*2*2*3*3*5

LCM=360

360-1=359 but the number of coins must be at least 500

the next common multiple of 10, 9, and 8 is 720

720-1=719

719 divided by 10 is 71 R9

719 divided by 9 is 79 R*8

719 divided by 8 is 89 R7

there are 719 coins in the chest