{"status": "success", "data": {"description_md": "When $p = \\sum\\limits_{k=1}^{6} k \\ln{k}$, the number $e^p$ is an integer.  What is the largest power of 2 that is a factor of $e^p$ ?\n\n$\\textbf{(A)}\\ 2^{12}\\qquad\\textbf{(B)}\\ 2^{14}\\qquad\\textbf{(C)}\\ 2^{16}\\qquad\\textbf{(D)}\\ 2^{18}\\qquad\\textbf{(E)}\\ 2^{20}$\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>When  <span class=\"katex--inline\">p = \\sum\\limits_{k=1}^{6} k \\ln{k}</span> , the number  <span class=\"katex--inline\">e^p</span>  is an integer.  What is the largest power of 2 that is a factor of  <span class=\"katex--inline\">e^p</span>  ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 2^{12}\\qquad\\textbf{(B)}\\ 2^{14}\\qquad\\textbf{(C)}\\ 2^{16}\\qquad\\textbf{(D)}\\ 2^{18}\\qquad\\textbf{(E)}\\ 2^{20}</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": 3, "problem_name": "2014 AMC 12B Problem 15", "can_next": true, "can_prev": true, "nxt": "/problem/14_amc12B_p16", "prev": "/problem/14_amc12B_p14"}}