Question

find the number nearest to 110000 but greater than 100000 which is exactly divisible by each of 8,15,and 21 .

Answer 1

LCM of 8 = $2^{3}$

LCM of 15 = 3 * 5

LCM of 21 = 3 * 7.


Therefore LCM of 8,15 and 21 = 2 * 2 * 2 * 3 * 5 * 7

                                                  = 840.


The number nearest to 110000 but > 100000 is 110000 / 840 = ~130.


Therefore the required number is 840 * 130

                                                         = 109200.


Hope this helps!

Answer 2

LCM of 8 = 2 * 2 * 2

LCM of 15 = 3 * 5

LCM of 21 = 3 * 7

LCM of 8,15,21 = 2^3 * 3 * 5 * 7

                         = 840.

Division Method:

840)110000(130

        840

        ----------

          2600

          2520

        -----------

             800

        ------------

Therefore the number nearest to 110000 but greater than 100000 that is divisible by 840 is 110000 - 800 = 109200.

The required number is 109200.

Hope this helps!