{"status": "success", "data": {"description_md": "How many positive integers $n$ are there such that $n$ is a multiple of $5$, and the least common multiple of $5!$ and $n$ equals $5$ times the greatest common divisor of $10!$ and $n?$\n\n$\\textbf{(A) } 12 \\qquad \\textbf{(B) } 24 \\qquad \\textbf{(C) } 36 \\qquad \\textbf{(D) } 48 \\qquad \\textbf{(E) } 72$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>How many positive integers  <span class=\"katex--inline\">n</span>  are there such that  <span class=\"katex--inline\">n</span>  is a multiple of  <span class=\"katex--inline\">5</span> , and the least common multiple of  <span class=\"katex--inline\">5!</span>  and  <span class=\"katex--inline\">n</span>  equals  <span class=\"katex--inline\">5</span>  times the greatest common divisor of  <span class=\"katex--inline\">10!</span>  and  <span class=\"katex--inline\">n?</span> </p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) } 12 \\qquad \\textbf{(B) } 24 \\qquad \\textbf{(C) } 36 \\qquad \\textbf{(D) } 48 \\qquad \\textbf{(E) } 72</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2020 AMC 12A Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/20_amc12A_p22", "prev": "/problem/20_amc12A_p20"}}