Answer: No number divided by 1 leaves a remainder of 1
since every number divides evenly by 1
divided by 2 leaving a remainder of 1:
1 , 3, 5, 7, 9, .... all odd numbers
divided by 3 leaving a remainder of 1:
1, 4, 7, 10, 13, 16, .....61 ....
divided by 4 leaves a remainder of 1:
1 , 5, 9, 13, 17, 21, ....61 ....
divided by 5 leaves a remainder of 1:
1, 6, 11, 16, 21, 26, 31, .... 61 ....
divided by 6 leaves a remainder of 1:
1, 7, 13, 19, ..... . 61 ....
looks like 61 , except the division by 1 part.
OR
LCM of 2,3,4,5 is 60
to have remainder of 1 for all
60 + 1 = 61