smc

By the definition of least common mutiple, we take the greatest powers of the prime numbers of the prime factorization of all the numbers, that we are taking the $\text{lcm}$ of. In this case, $$M=2^4\cdot 3^3\cdot 5^2\cdot 7\cdot 11\cdot 13\cdot 17\cdot 19\cdot 23\cdot 29.$$ Now, using the same logic, we find that $$N=M\cdot 2\cdot 37,$$ because we have an extra power of $2$ and an extra power of $37.$ Thus, $\frac{N}{M}=2\cdot 37=\boxed{74}.$