Expressing in base 5 has final digit 0. So, it has to be a multiple of 5.
Expressing in base 8 notation has 1 as leftmost digit. So, it has to be (1xy) in base 8.
So, the number varies from 100 to 127 (177 in base 8 = 127 in base 10).
Expressing in base 11 notation, 1 is the left most digit. Again, it has to be (1ab) in base 11.
So, the integer is greater than 121 (100 in base 11 = 121 in base 10).
Combining three conditions, we get the number as 125.
∴(1257), remainder = 6.