The best thing to do is to look for a pattern.

If $k=1$ we want $x\equiv 1 \pmod{2}$, so clearly $x = 1$ works.

If $k=2$ we want $x\equiv 1\pmod{2}$ and $x\equiv 2\pmod{3}$, so we can see that $x=5$ works.

If $k=3$ we want  $x\equiv 1\pmod{2}$, $x\equiv 2\pmod{3}$, and $x\equiv 3\pmod{4}$, so we can see that $x=11$ works.

I'll let you work out some more examples (try to find the smallest $x$ in each case). Then think about how:  $1$ relates to the set of numbers $\{2\}$, $5$ relates to the set of numbers $\{2,3\}$, $11$ relates to the set of numbers $\{2, 3, 4\}$, etc.

Let us know if you have any other questions or need more of a hint.