// Numbas version: exam_results_page_options
{"name": "LCM and HCF", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "LCM and HCF", "tags": [], "metadata": {"description": "Calculating the LCM and HCF of numbers by using prime factorisation.", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>$x = \\var{x}$</p>\n<p>$y = \\var{y}$</p>\n<p>$z = \\var{z}$</p>\n<p></p>\n<p>By considering the prime factorisation of $x, y $ and $z$, or otherwise, find:</p>", "advice": "<p>We can write $x,y,z$ as a product of prime factors as follows:</p>\n<p>$x=\\var{x}=\\var{show_factors(x)}$</p>\n<p>$y=\\var{y}=\\var{show_factors(y)}$</p>\n<p>$z=\\var{z}=\\var{show_factors(z)}$</p>\n<p></p>\n<p>For&nbsp;HCF of $\\var{x}$ and $\\var{y}$ we need to multiply each factor the least number of times it occurs in either $\\var{x}$ or $\\var{y}$</p>\n<p>i.e. HCF$(x,y) = \\var{show_factors(hcf_xy)}=\\var{hcf_xy}$</p>\n<p></p>\n<p>For&nbsp;LCM of $\\var{x}$ and $\\var{y}$ we need to multiply each factor the greatest number of times it occurs in either $\\var{x}$ or $\\var{y}$</p>\n<p>i.e. LCM$(x,y) = \\var{show_factors(lcm_xy)}=\\var{lcm_xy}$</p>\n<p></p>\n<p>For&nbsp;HCF of $\\var{x}$ and $\\var{z}$ we need to multiply each factor the least number of times it occurs in either $\\var{x}$ or $\\var{z}$</p>\n<p>i.e. HCF$(x,z) = \\var{show_factors(hcf_xz)}=\\var{hcf_xz}$</p>\n<p></p>\n<p>For&nbsp;LCM of $\\var{x}$ and $\\var{z}$ we need to multiply each factor the&nbsp;greatest&nbsp;number of times it occurs in either $\\var{x}$ or $\\var{z}$</p>\n<p>i.e. LCM$(x,z) = \\var{show_factors(lcm_xz)}=\\var{lcm_xz}$</p>\n<p></p>\n<p>For HCF of $\\var{x},\\var{y}$ and $\\var{z}$ we need to multiply each factor the least number of times it occurs in either $\\var{x}$ or $\\var{y}$&nbsp;or $\\var{z}$</p>\n<p>i.e. HCF$(x,y,z) = 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