How to find the least $N$ such that $N \equiv 7 \mod 180$ or $N \equiv 7 \mod 144$ but $N \equiv 1 \mod 7$? How to approach this problem:

N is the least number such that $N \equiv 7 \mod 180$  or $N \equiv 7 \mod 144$  but $N \equiv 1 \mod 7$.Then which of the these is true:



*

*$0 \lt N \lt 1000$

*$1000 \lt N \lt 2000$

*$2000 \lt N \lt 4000$

*$N \gt 4000$


Please explain your idea.
ADDED: The actual problem which comes in my paper is "or" and the "and" was my mistake but I think I learned something new owing to that.Thanks all for being patient,and appologies for the inconvenience.

I assume that the question is "or."  Then it is simplest to just compute the answer.
Notice that $180 \equiv 5 \pmod{7}$ and $144\equiv 4 \pmod{7}$.  Since $3\cdot 5\equiv 1\pmod 7$, we see that $3\cdot 180+7\equiv 1\pmod{7}$.  Also, since $2\cdot4\equiv 1\pmod{7}$ we also have $2\cdot144 +7\equiv 1\pmod{7}$.  As the smaller of the two is the second, we conclude that $N=295$.
