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

In order to find out the two nearest numbers which are divisible by 2,3,4,5,6,7 firstly we have to find the LCM of 2,3,4,5,6,7 as:

So, LCM of 2,3,4,5,6,7 = 2 × 2 × 3 × 5 × 7 = 420

Now, the division of 10000 by 420 is carried out as:

So, on dividing 10000 by 420, we get 340 as the remainder.

Therefore, the number which is divisible by each of 2,3,4,5,6,7 and nearest to 10000 = 10000 - 340 = 9660

The other number which is divisible by each of 2,3,4,5,6,7 and nearest to 10000 is obtained by multiplying 420 with the number which is successor of quotient i.e., 24.

∴ 420 × 24 = 10080

Hence, the two numbers which are nearest to 10000 and are divisible by each of 2,3,4,5,6,7 are 9660 and 10080 respectively.

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