Find the greatest 4-digit number which when increase by 1 is exactly divisible by 2,3,4,5,6 and 7.

Find the greatest 4-digit number which when increase by 1 is exactly divisible by 2,3,4,5,6 and 7.
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1 Answer

LCM of the numbers is 420. To find the greatest 4-digit number we find a multiple of 420 close to and less than 10000. 10000/420=23 to the nearest lower integer. 23×420=9660, so the largest 4-digit number is 9660 divisible by the given set of divisors. Subtract 1 to give 9659. When 1 is added to this we get a number divisible exactly by each divisor.

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