{"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$\\textbf{(A)}\\ 2\\qquad\\textbf{(B)}\\ 3\\qquad\\textbf{(C)}\\ 4\\qquad\\textbf{(D)}\\ 5\\qquad\\textbf{(E)}\\ 7$", "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;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2018 AMC 10A Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/18_amc10A_p18", "prev": "/problem/18_amc10A_p16"}}