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My question is: Given that the equation $\,\frac{8}{3}x - a = \frac{9}{4}x + 123\,$ has positive integral solution where a is also positive integer, find the minimum possible value of a.

Please any guidance to solve this question would be helpful as even after trying a lot I was unable to solve it.

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    @DonAntonio:Thanks the edit you made is correct.2012-06-02

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I'll assume you meant $\frac{8}{3}x-a=\frac{9}{4}x+123\Longleftrightarrow\frac{5}{12}x=123+a\Longleftrightarrow x=\frac{12\cdot 123+12a}{5}$ As $\,12\cdot 123\,$ ends with a $\,6\,$, we need $\,12a\,$ to end with a $\,4\,$ (to have a multiple of $\,5\,$), and that happens for $\,a=2\,$

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    @Andre That indeed looks both more elegant and clear.2012-06-02