Question

Determine the two numbers nearest to 1000 which are exactly divisible by each of 2,3,5 and 6

Answer 1

Solution : The smallest number which is exactly divisible by 2,3,4,5,6 and 7 is their LCM. 
LCM of 2,3,4,5,6 and 7 = 420
The number nearest to 10,000 and exactly divisible by each given numbers
should also be exactly divisible by their LCM 420.
So divide 10,000 by 420.


We find the remainder is 340.
Number just less than 10,000 and exactly divisible by 420
= 10000 -340 =9660
Number just greater than 10,000 and exactly divisible by 420
= 10000 + (420 - 340) = 10080 
Hence, the required numbers are 9660 and 10080.
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