Brain Teaser - Answer.

The "Least Common Multiple" of 2, 3,4,5,6 is 60
In 2's = 60 x2 +1 = 121
In 3's = 60 x3 +1 =181
In 4's = 60 x4 +1 =241
In 5's = 60 x5 +1 =301
In 6's = 60 x6 +1 =361
We know that the answer should be in multiples of 7.
Hence from the above, 301 is the only least number fully divisible by 7.
The Least Common Multiple of 2, 3, 4,5,6,7 is 420
Hence the answers should be 301+420+420..... so on.