Question

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

Answer 1

answer file is attached. the number is 109200. 

Answer 2

Answer:

The number that is near to the 110000 and should be greater than 100000 and also that should be divisible by 8, 15 and 21 is 109200.

To find:  

The number that is near to the 110000 and should be greater than 100000 and also that should be divisible by 8, 15 and 21.

Solution:

The LCM (8, 15 and 21) is

$\begin{array} { c } { 8 = 2 \times 2 \times 2 } \\\\ { 15 = 3 \times 5 } \\\\ { 21 = 3 \times 7 } \end{array}$

LCM of 8, 15 and 21

$= 2 \times 2 \times 2 \times 3 \times 5 \times 7 = 840$

LCM of 8, 15 and 21 = 840

If we divide 110000 by 840, we will get remainder as 800. Hence 110000 is not exactly divisible by 840.

Now we need to subtract the number 840 from 110000 and we will get the exact number and the resultant number is divisible by 8, 15 and 21.

110000-840

=109200

The number nearer to 110000 and greater than 100000 and also that should be divisible by 8, 15 and 21 is 109200.