Question

find the gretest number which of 6 digits exactly divided by 24,15 and 36

Answer 1

First let us find the LCM of the above numbers,
So the LCM is 360.
Then we have to divide the greatest 6 digit no. 999999 by 360
So the remainder is 279 . Then subtract it from 999999. So you will get the largest 6 digit no. Divisible by the above numbers is 999720.


Hope it helps

Answer 2

Solution :

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Given :

To Find the greatest number which of 6 digits exactly divided by 24,15 and 36.

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We know that,

LCM of integers is divisible by all its constituents,.

Hence,.

By finding LCM  of 24, 15 & 36 and DIviding it by the largest six digit number (999,999)  by removing the remainder, we will be able to find the greatest 6 digit number exactly divisible by 24,15 & 36,.

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The steps are as Follows :

⇒ LCM{24,15,36}

2 L 24 , 15, 36
   l------------------
2 L 12, 15 , 18
   l-----------------
2 L 6, 15 , 9
   l-----------------
3 L 3 , 5 , 9
   l-----------------
   l 1 , 5 , 3
  
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LCM{24, 15, 36} = 2 × 2 × 2 × 3 × 3 × 5

⇒ 8 × 9 × 5

⇒ 72 × 5

⇒ 360

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By dividing it by greatest 6 digit number we get,.

⇒ 999,999 = 360 × 2777 + 279

Hence, By removing remainder we get,

⇒ 999,999 - 279 = 999,720

                          ∴ The greatest 6 digit number divisible by 24, 15 & 36 is 999,720
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                                           Hope it Helps !!