{"status": "success", "data": {"description_md": "Let $S$ be a set of $6$ integers taken from $\\{1,2,\\ldots,12\\}$ with the property that if $a$ and $b$ are elements of $S$ with $a<b$, then $b$ is not a multiple of $a$. What is the least possible value of an element in $S$?\n\n$\\textbf{(A)}\\ 2\\qquad\\textbf{(B)}\\ 3\\qquad\\textbf{(C)}\\ 4\\qquad\\textbf{(D)}\\ 5\\qquad\\textbf{(E)}\\ 7$\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>Let  <span class=\"katex--inline\">S</span>  be a set of  <span class=\"katex--inline\">6</span>  integers taken from  <span class=\"katex--inline\">\\{1,2,\\ldots,12\\}</span>  with the property that if  <span class=\"katex--inline\">a</span>  and  <span class=\"katex--inline\">b</span>  are elements of  <span class=\"katex--inline\">S</span>  with  <span class=\"katex--inline\">a&lt;b</span> , then  <span class=\"katex--inline\">b</span>  is not a multiple of  <span class=\"katex--inline\">a</span> . What is the least possible value of an element in  <span class=\"katex--inline\">S</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 2\\qquad\\textbf{(B)}\\ 3\\qquad\\textbf{(C)}\\ 4\\qquad\\textbf{(D)}\\ 5\\qquad\\textbf{(E)}\\ 7</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": "2018 AMC 12A Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/18_amc12A_p13", "prev": "/problem/18_amc12A_p11"}}