{"status": "success", "data": {"description_md": "How many ordered triples $(x,y,z)$ of positive integers satisfy $\\text{lcm}(x,y) = 72, \\text{lcm}(x,z) = 600$ and $\\text{lcm}(y,z)=900$?\n\n$\\textbf{(A)}\\ 15\\qquad\\textbf{(B)}\\ 16\\qquad\\textbf{(C)}\\ 24\\qquad\\textbf{(D)}\\ 27\\qquad\\textbf{(E)}\\ 64$\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>How many ordered triples  <span class=\"katex--inline\">(x,y,z)</span>  of positive integers satisfy  <span class=\"katex--inline\">\\text{lcm}(x,y) = 72, \\text{lcm}(x,z) = 600</span>  and  <span class=\"katex--inline\">\\text{lcm}(y,z)=900</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 15\\qquad\\textbf{(B)}\\ 16\\qquad\\textbf{(C)}\\ 24\\qquad\\textbf{(D)}\\ 27\\qquad\\textbf{(E)}\\ 64</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": 5, "problem_name": "2016 AMC 12A Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/16_amc12A_p23", "prev": "/problem/16_amc12A_p21"}}