AMC 12 2019b Problem 5

Each piece of candy in a store costs a whole number of cents. Casper has exactly enough money to buy either $12$ pieces of red candy, $14$ pieces of green candy, $15$ pieces of blue candy, or $n$ pieces of purple candy. A piece of purple candy costs $20$ cents. What is the smallest possible value of $n$?

$\textbf{(A) } 18 \textbf{(B) } 21 \textbf{(C) } 24 \textbf{(D) } 25 \textbf{(E) } 28$