Question

what will be the least number divided by3,4,6and 9 leaves a
remainder 2,but when divided by 11 leaves no remainder

Answer 1

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