Grade 8 - Number Theory #2

Find the natural number $N$ that satisfies the three conditions below.

• $N$ is a three-digit odd number.
• $\dfrac{N}{630}$ is a terminating decimal.
• If $M=\dfrac{4N}{63}$ , then $M$ is a square of a natural number.

This problem is a part of <Grade 8 - Number Theory> series .