What is the smallest positive integer that leaves a remainder of 1 when divided by 2, 3, 4, 5, or 6, but has no remainder when divided by 7?
301
The least common multiple of 2, 3, 4, 5, and 6 is 60. The candidate numbers are of the form 60k + 1 (61, 121, 181, 241, 301...). 301 is the first such number evenly divisible by 7 (7 * 43 = 301).
About this riddle
Math riddles hide a calculation inside a short story. Pull out the numbers, work out what is being asked, and watch for a trick such as a unit change.
Difficulty: Hard. More like this: Math riddles with answers or try Target 24 for a different kind of puzzle.
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