The least common multiple of a number n and 6 is 42 what are all of the possible whole number values for n

I did it with "tries & mistakes" method:

n is not 1, because LCM of 1 and 6 is 6
n is not 2, because LCM of 2 and 6 is 6
n is not 3, because LCM of 3 and 6 is 6
n is not 4, because LCM of 4 and 6 is 12
n is not 5, because LCM of 5 and 6 is 30
n is not 6, because LCM of 6 and 6 is 6
n might be 7, because LCM of 7 and 6 is what we're looking for - 42.
n might be also 14 or 21 - so these are all multiplies of 7 which are less or equal to half of 42.

I hope it helps :)