Question

Find the least number which leaves remainder 1 when divided by 2,3,4,5 or 6 but is completely divisible by 7

Answer 1

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Explanation:

We're looking for a number that is divisible by 2, 3, 4, 5, and 6 (meaning that N is a multiple of those numbers) and that number +1 being divisible by 7.

We can make progress on this by seeing that the Lowest Common Multiple of these numbers is

2×2×3×5=60.

Now the key is to find a multiple of 60 such that when we add 1 to it, the number becomes divisible by 7.

After some trial and error, I found that the lowest number that works is 300, which is

5×60

When we take

300+1=301,

301÷7=43 .

So, the answer is 301.

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