division by 45 16 as Quitni 9 reminder
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Let Z be the number
Z = 13x + 11 where x is the quotient when Z is divided by 13
Z = 17y + 9 where y is the quotient when Z is divided by 17
13x + 11 = 17y + 9
13x + 2 = 17y since x and y are quotients they should be whole numbers . Since y has to be a whole number the left hand side should be multiple of 17
The least possible value of x satisfying the condition is 9 and y will be 7
The answer is 13*9 + 11 = 128 or it is 17*7 + 9 = 128
This is the least number possible. There will be multiple answers and will increase in multiples 17*13 = 221 like 349 , 570, etc
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