# Find the least number which when divided by 5,6,7 & 8 leaves a remainder 3, but when divided by 9 leaves no remainder.

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by papia75

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by papia75

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1683 is the number.............

so it is 3 more than multiples ot LCM of 5 6 7 8

now LCM of 5 6 7 8

factorisee

5 = 5

6 = 2*3

7 = 7

8 = 2* 2* 2 = 2^3

LCM = 5*2^3*3*7 = 840

now it has to be of the form 840n + 3

this is divisible by 9

840n + 3 = 9m

3 = 9m - 840n

now using extended euler algorithm

we need to find GCD of 840 and 9

840 = 9*93 + 3

3= 840*1 - 9*93

so n = -1 or 2 as it is mod 3

so 840*n +3 = 1683 divisible by 9

hence ans is 1683