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