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{"name": "21.c LCM of two numbers", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "21.c LCM of two numbers", "tags": [], "metadata": {"description": "<p>Calculating the LCM of two numbers by using prime factorisation.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>By considering the prime factorisation of $\\var{x}$ and $\\var{y}$, or otherwise, find the lowest common multiple (LCM) of $\\var{x}$ and $\\var{y}$.</p>", "advice": "<p>We can write $\\var{x}$ and $\\var{y}$ as a product of prime factors as follows:</p>\n<p>$\\var{x}=\\var{show_factors(x)}$</p>\n<p>$\\var{y}=\\var{show_factors(y)}$.</p>\n<p></p>\n<p>For 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><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Factors\"><span style=\"font-weight: 400;\">Use this link to find some resources which will help you revise this topic.</span></a></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"x": {"name": "x", "group": "Ungrouped variables", "definition": "random(2..70)", "description": "", "templateType": "anything", "can_override": false}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "random(2..70)", "description": "", "templateType": "anything", "can_override": false}, "lcm_xy": {"name": "lcm_xy", "group": "Ungrouped variables", "definition": "lcm(x,y)", "description": "", "templateType": "anything", "can_override": false}, "primes": {"name": "primes", "group": "Ungrouped variables", "definition": 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