what is the smallest number that leaves a remainder of 5 when divided by 12,14,and 18

What is the smallest number that leaves a remainder of 5 when divided by 12, 14, and 18?

 

First, find the smallest number that is divisible by 12, 14, and 18:

   ---  factor each of the numbers:

                   12  =  2 x 2 x 3

                   14  =  2 x 7

                   18  =  2 x 3 x 3

  ---  the least common multiple of these numbers is  2 x 2 x 3 x 3 x 7  =  252

Thus, 252 is divisible by 12, 14, and 18.

 

If you want a remainder of 5, add 5 to that number:  252 + 5  =  257.