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

1
by papia75

2015-06-06T22:59:30+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
1683 is the number.............
devided by 5 6 7 8 it leaves 3

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
mark my answer as brainliest and click on yellow button
hahhaaha
copy pasted....
nice carry on