Math, asked by Rahul2030, 9 months ago

The greatest five digit number, when divided by 8,9 and 10 leaves remainder 2 is ​

Answers

Answered by amitnrw
3

Given : number, when divided by 8,9 and 10 leaves remainder 2

To find : Greatest five Digit Number

Solution:

Number   when divided by 8,9 and 10 leaves remainder 2 is ​

=> N  = 8A + 2

=> N = 9B  + 2

=> N = 10C  + 2

=> N - 2 = 8A  = 9B = 10C

Hence N -2 will have a factor which will be LCM of  8 , 9 & 10

LCM of 8 , 9 & 10

8 = 2 * 2 * 2

9 = 3 * 3

10 = 2 * 5

LCM = 2 * 2 * 2 * 3 * 3 * 5  = 360

=> N - 2 = 360K

=> N = 360K  + 2

99999/360  > 277

=> N = 360 * 277  + 2

=> N = 99722

99722 is greatest five digit number, when divided by 8,9 and 10 leaves remainder 2

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Answered by rohitkumargupta
1

Answer:  

Answer:  Step-by-step explanation:  HELLO DEAR,

Given: 8,9,10 is number ,where each number  divide greatest five digit number and leave remainder 2.

Subject : To find greatest five digit number which divide by 8,9,10 then leave remainder 2.

 Solution: Let the number be X.              

  As per question , when 8 divide X then it leave remainder 2.                

We can write it in mathematical  form ,                    X= 8a + 2.          ( where a is quotient )                    X- 2= 8a                  

Like above we can write two other relations,                  X= 9b + 2.                 X-2 = 9b            And ,.           X= 10c + 2         X - 2= 10c.

From the above relation we can conclude that LCM of 8,9,10 is the factor of N-2.

So, LCM of 8,9,10.  

8= 2×2×2

  9=3×3

  9=3×310=2×5.

  9=3×310=2×5.-------------------

  9=3×310=2×5.-------------------LCM= 2×2×2×3×3×5        = 360.

Therefore,

Therefore,(N-2)/360 = k.

Therefore,(N-2)/360 = k.N- 2= 360k

Here ,there is a point to understand ,k is always less than the (99999)/360.

So, 99999/360>k       99999/360 >277.

Therefore by putting value k= 277 we get that number.

   N- 2= 360×277

   N= 360×277 +2  

N= 99720 + 2  

N= 99722 Answer.

I HOPE IT HELP YOU DEAR,

THANKS.

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