{"status": "success", "data": {"description_md": "Define $L_n$ as the least common multiple of all the integers from $1$ to $n$ inclusive. There is a unique integer $h$ such that\n$$\\frac{1}{1}+\\frac{1}{2}+\\frac{1}{3}+\\cdots+\\frac{1}{17}=\\frac{h}{L_{17}}$$\nWhat is the remainder when $h$ is divided by $17$?\n\n$\\textbf{(A) } 1 \\qquad \\textbf{(B) } 3 \\qquad \\textbf{(C) } 5 \\qquad \\textbf{(D) } 7 \\qquad \\textbf{(E) } 9$", "description_html": "<p>Define  <span class=\"katex--inline\">L_n</span>  as the least common multiple of all the integers from  <span class=\"katex--inline\">1</span>  to  <span class=\"katex--inline\">n</span>  inclusive. There is a unique integer  <span class=\"katex--inline\">h</span>  such that<br/>\n <span class=\"katex--display\">\\frac{1}{1}+\\frac{1}{2}+\\frac{1}{3}+\\cdots+\\frac{1}{17}=\\frac{h}{L_{17}}</span> <br/>\nWhat is the remainder when  <span class=\"katex--inline\">h</span>  is divided by  <span class=\"katex--inline\">17</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } 1 \\qquad \\textbf{(B) } 3 \\qquad \\textbf{(C) } 5 \\qquad \\textbf{(D) } 7 \\qquad \\textbf{(E) } 9</span> </p>\n<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": "2022 AMC 10A Problem 19", "can_next": true, "can_prev": true, "nxt": "/problem/22_amc10A_p20", "prev": "/problem/22_amc10A_p18"}}