Find the two numbers nearest to 10000 which are exactly divisible by each of 2, 3, 4, 5, 6 and 7?

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9660, 10080

9320, 10080

9660, 10060

10340, 10080

answer is A.

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Detailed Solution

The numbers which are exactly divisible by 2, 3, 4, 5, 6 and 7 are the multiples of the LCM of the given numbers.
∴ LCM = 2 x 2 x 3 x 5 x 7 = 420
Now, dividing 10000 by 420, we get remainder = 340
∴ Number less than 10000 and exactly divisible by the given numbers = 10000 - 340 = 9660
Number greater than 10000 and exactly divisible by the given numbers = 10000 + (420 - 340) = 10080

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