2021 Fall AMC 12A Problem 8

$M = \operatorname{lcm}(10, \ldots, 30)$ contains $2^4$ (from $16$), $3^3$ (from $27$), $5^2$ (from $25$), $7,$ and every prime up to $29.$ Among $32, \ldots, 40,$ the only new contributions are $32 = 2^5,$ which raises the power of $2$ from $2^4$ to $2^5,$ and the new prime $37.$ Everything else factors into primes and powers already in $M.$ Therefore $\dfrac{N}{M} = 2 \cdot 37 = 74.$ Thus, the correct answer is D.