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find the smallest number which when divided by 9,11,13 leaves the remainder 1,2,3 respestively

find the smallest number which when divided by 9,11,13 leaves the remainder 1,2,3 respestively

Grade:10

1 Answers

Yash SIngh
34 Points
6 years ago
let the no be x;
x=9a+1;
x=11b+2; 
x=13c+3;
multiply all equations by 2:
2x=9d+2;
2x=11e+4;
2x=13f+6;
now add 7 to all;
2x+7=9d+9;     divisible by 9
2x+7=11e+11;    divisible by 11
2x+7=13f+13;    divisible by 13
therefore LCM(9,11,13)=2x+7
(9*11*13-7)/2=x
=>x=640, if not 640 then keep multiplying by 2,3,4,5,6,etc
we take LCM because it is the smallest no which has 9,11,13 as factor
 

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