jmc

First, we prime factorize the given numbers: $$10=2\cdot 5,14=2\cdot 7,70=2\cdot 5\cdot 7.$$ Since the least common multiple of $10$ and $14$ is already $70$ ($2\cdot 5\cdot 7$), we can maximize $x$ by letting it be $\boxed{70}$.