Remainder when dividing by a given number

A number when divided by 17 leaves 12 as remainder while on dividing by 11 leaves 8 as remainder.The remainder that it leaves on dividing by 23 is

What is the smallest number which leaves remainder 3 when divided by any of the numbers 5, 6 or 8 but leaves no remainder when it is divide by 9 ?

The remainder on dividing given integers a and h by 7 are respectively 5 and 4. What is the remainder when ab is divided by 7 ?

A number when divided by 3, 4, 5 and 6 always leaves remainder of 2, but leaves no remainder when divided by 7. What is the lowest such number possible ?

A number N when divided by 14 given the remainder 5. What is the remainder when the same number is divided by 7?

A number when divided by 10 leaves a remiander 9, when divided by 9 leaves a remainder 8, when divided by 8 leaves a remainder 7 ............ When divided by 2 leaves a remainder 1. Determine the number.