Question

find the greatest number of four digits, which is exactly divisible by 18 ,24and 45.​

Answer 1

question: find the greatest number of four digits, which is exactly divisible by 18 ,24and 45.​

answer:

To find the greatest 4 digit number which is exactly divisible by 12, 18, 40 and 45, first we have to compute the LCM of 12, 18, 40 and 45.

           _______________  

       2  | 12, 18, 40, 45

           |_______________

       2  |   6,  9,  20, 45  

           |_______________

       2  |   3,  9,  10, 45

           |_______________

       3  |   3,  9,   5,  45  

           |_______________

       3  |   1,  3,   5,  15

           |_______________

       5  |   1, 1,    5,   5

           |_______________

           |   1, 1,    1,   1

The LCM of 12, 18, 40 and 45 = 2*2*2*3*3*5 = 360

Now, we will divide the greatest 4 digit number by 360.

The greatest 4 digit number is 9999.

           ______

     360) 9999 (27

             720

           _____

             2799

             2520

          ______

               279 - Remainder

          ______

Now, we have to subtract the remainder, which is 279, from 9999.

⇒ 9999 - 279 = 9720

So, 9720 is the required greatest 4 digit number which is exactly divisible by 12, 18, 40 and 45.

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