{"status": "success", "data": {"description_md": "There are exactly $77,000$ ordered quadruplets $(a, b, c, d)$ such that gcd$(a, b, c, d) = 77$ and lcm$(a, b, c, d) = n$. What is the smallest possible value for $n$?\n\n$\\textbf{(A)}\\ 13,860\\qquad\\textbf{(B)}\\ 20,790\\qquad\\textbf{(C)}\\ 21,560 \\qquad\\textbf{(D)}\\ 27,720 \\qquad\\textbf{(E)}\\ 41,580$\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>There are exactly <span class=\"katex--inline\">77,000</span> ordered quadruplets <span class=\"katex--inline\">(a, b, c, d)</span> such that gcd<span class=\"katex--inline\">(a, b, c, d) = 77</span> and lcm<span class=\"katex--inline\">(a, b, c, d) = n</span>. What is the smallest possible value for <span class=\"katex--inline\">n</span>?</p>&#10;<p><span class=\"katex--inline\">\\textbf{(A)}\\ 13,860\\qquad\\textbf{(B)}\\ 20,790\\qquad\\textbf{(C)}\\ 21,560 \\qquad\\textbf{(D)}\\ 27,720 \\qquad\\textbf{(E)}\\ 41,580</span></p>&#10;<hr/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2016 AMC 12B Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/16_amc12B_p25", "prev": "/problem/16_amc12B_p23"}}