A number can be divided by 11. This number plus 1 is a multiple of 3,5,7,9. What is this number?

A number can be divided by 11. This number plus 1 is a multiple of 3,5,7,9. What is this number?

The least common multiple of 3,5,7,9 is 5 × 7 × 9 = 315
315-1=314
This number can be divided by 11, that is, 314 plus an integral multiple of 315 can be divided by 11
314 △ 11 = 28,6
315 △ 11 = 28,7
6 + 7 × 7 = 55 can be divided by 11
So the minimum number is 314 + 315 × 7 = 2519