2020 AMC 10B Problem 15

Steve wrote the digits 1, 2, 3, 4, and 5 in order repeatedly from left to right, forming a list of 10,000 digits, beginning 123451234512\ldots. He then erased every third digit from his list (that is, the 3rd, 6th, 9th, \ldots digits from the left), then erased every fourth digit from the resulting list (that is, the 4th, 8th, 12th, \ldots digits from the left in what remained), and then erased every fifth digit from what remained at that point. What is the sum of the three digits that were then in the positions 2019, 2020, 2021?

\textbf{(A)}\ 7 \qquad\textbf{(B)}\ 9 \qquad\textbf{(C)}\ 10 \qquad\textbf{(D)}\ 11 \qquad\textbf{(E)}\ 12

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.