Question

It x, y, and z are positive intergers and 3x = 4y = 7z, then the least possible value of x + y + z is???

For the ones who were mad because I asked a dumb question i was just testing if this thing work, because I'm doing high school homework and it's so hard​

Answer 1

`3x = 4y = 7z \\ \Rightarrow \begin{cases}3x - 4y = 0 \\4y - 7z = 0 \\ 7z - 3x = 0\end{cases} \\ \Leftrightarrow \begin{cases}x = (4)/(3) y\\4y - 7z = 0 \\ 7z - 3( (4)/(3)y) = 0\end{cases} \\ \Leftrightarrow \begin{cases}x = (4)/(3) y\\4y - 7z = 0 \\ 7z - 4y= 0\end{cases} \\ \Leftrightarrow \begin{cases}x = (4)/(3) y\\ y \\ z = (4)/(7)y \end{cases} \\ x,y,z\: are\: intergers\Rightarrow y=LCM(3,7)=21\Rightarrow x = 28,z = 12 \\ \Rightarrow x + y + z = 61`