What is the smallest positive integer which gives 1 as a remainder when divided by the numbers 2,3,4,5,6

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  1. The LCM is 60
    So how about 61 as the lowest number.

    for the 2 it would be 3,5,7,9,11,13,....,57,59,61,63,..
    for the 3 it would be 4,7,10,13,16,....,58,61,64,...
    for the 4 it would be 5,9,13,17,...., 49,53,57,61,65,...
    for the 5 it would be 6,11,16,....., 51,56,61,66,....
    for the 6 it would be 7, 13,19,...., 49,55,61,67,...

    For a while I was cheering for 13, but it looks like 61 is the winner.

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