Question

how many numbers are there between 200 and 300 which are exactly divisible by 6,8 and 9​

Answer 1

Answer:

There is only 2 number between 200 and 300 which can exact divide by 6, 8 and 9.

Step-by-step explanation:

First we need to take out the LCM of 6, 8 and 9.

LCM of 6, 8 and 9 is 72.

Now, Divide 200 by 72.

=> 200/ 72

=> 2.777777

Just take the value before point. So, we take number 2.

Now, Divide 300 by 72.

=> 300/ 72

=> 4.1666666

Just take the value before point. So, we take number 4.

So, Subtract the 2 from 4.

=> 4 - 2

=> 2

So, there is only 2 number between 200 and 300 which can exact divide by 72 or 6, 8 and 9.

Answer 2

There are exactly "two (2) numbers", which is divisible by 6, 8 and 9​.

Step-by-step explanation:

We have,

200 and 300

To find, total number of numbers exactly divisible by 6, 8 and 9​ = ?

LCM(6, 8 and 9)

6 = 2 × 2

8 = 2 × 2 × 2 and

9 = 3 × 3

∴ The LCM(6, 8 and 9) = 2 × 2 × 2 × 3 × 3 = 72

The multiplles of 72 are:

72, 144, 216, 288, 360

The numbers are between 200 and 300 which are exactly divisible by 6, 8 and 9​ = 216, 288

Thus, there are exactly "two (2) numbers", which is divisible by 6, 8 and 9​.