{"status": "success", "data": {"description_md": "Given fractions $\\frac{a}{15}$ and $\\frac{b}{21}$ that are already in lowest terms (i.e. $\\frac{a}{15}$ and $\\frac{b}{21}$ cannot be reduced further), find the smallest value of the denominator of $\\frac{a}{15}+\\frac{b}{21}$, when the new fraction is reduced.\n\n$\\textbf{(A)}~3 \\qquad \\textbf{(B)}~5 \\qquad \\textbf{(C)}~7 \\qquad \\textbf{(D)}~35 \\qquad \\textbf{(E)}~105$ ", "description_html": "<p>Given fractions <span class=\"katex--inline\">\\frac{a}{15}</span> and <span class=\"katex--inline\">\\frac{b}{21}</span> that are already in lowest terms (i.e. <span class=\"katex--inline\">\\frac{a}{15}</span> and <span class=\"katex--inline\">\\frac{b}{21}</span> cannot be reduced further), find the smallest value of the denominator of <span class=\"katex--inline\">\\frac{a}{15}+\\frac{b}{21}</span>, when the new fraction is reduced.</p>&#10;<p><span class=\"katex--inline\">\\textbf{(A)}~3 \\qquad \\textbf{(B)}~5 \\qquad \\textbf{(C)}~7 \\qquad \\textbf{(D)}~35 \\qquad \\textbf{(E)}~105</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "2024 Mock AMC 10 - Problem 5", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}