What is the smallest number when divided by 2 remaining of 1 divided by 3 remaining of 2 divided by 4 remaining of 3 divided by 5 remaining of 4 and divided by 6 remaining 5?

Answer 1

The number is 59.

Note that the LCM of 2, 3, 4, 5, and 6 is 60

60 = 2*2*3*5

so 59 = 60-1 should leave the given remainders:

59 = 2*29 + 1 (remainder=1)

59 = 3*19 + 2 (remainder=2)

59 = 4*14 + 3 (etc)

59 = 5*11 + 4

59 = 6*9 + 5