Question

find the smallest number which
h divided by8,9,10,15,20,gives remainder of 5 every time

Answer 1

Final answer will be 360.

Answer 2

962
Here's how you approach such questions. First find the lcm of the numbers that the required number is divisible with, i.e., 3,5,6,8,10,12 which is 120

Therefore the required number is of the form 120x+2 (since it leaves a reminder of 2)

Now the number is a multiple of 13. 
so 120x+2 is a multiple of 13
=> 117x + 3x+2 is a multiple of 13

The least value of x for which this holds true is 8 (3*8+2 = 26)
Therefore the least such number is 120*8+2 = 962