{"status": "success", "data": {"description_md": "Let $[r,s]$ denote the least common multiple of positive integers $r$ and $s$. Find the number of ordered triples $(a,b,c)$ of positive integers for which $[a,b] = 1000$, $[b,c] = 2000$, and $[c,a] = 2000$\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full 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\">[r,s]</span> denote the least common multiple of positive integers <span class=\"katex--inline\">r</span> and <span class=\"katex--inline\">s</span>. Find the number of ordered triples <span class=\"katex--inline\">(a,b,c)</span> of positive integers for which <span class=\"katex--inline\">[a,b] = 1000</span>, <span class=\"katex--inline\">[b,c] = 2000</span>, and <span class=\"katex--inline\">[c,a] = 2000</span></p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. 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": 4, "problem_name": "1987 AIME Problem 7", "can_next": true, "can_prev": true, "nxt": "/problem/87_aime_p08", "prev": "/problem/87_aime_p06"}}