Positive integers $x$,$y$,$z$ If $x$ , $y$ and $z$ are positive integers and $3x = 4y = 7z$, then calculate the smallest possible value for $x+y+z$.
How do you do this? Can someone please give me a hint?

Consider $N = 3x = 4y = 7z$. $N$ is known to have divisors $3$, $4$ and $7$. The smallest positive $N$ that has these $3$ divisors is $84$.
And since $N, x, y, z$ and $x+y+z$ are all related by constant ratios, the smallest $N$ gives the smallest $x+y+z$.
