Question

Find two numbers nearest to 10000 which are exactly divisible by each of 16,28,40 and 56.​

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

= 10000340 =9660

Number just greater than 10,000 and exactly divisible by 420

= 10000 + (420 - 340) = 10080

Hence, the required numbers are 9660 and 10080.