70: $2, 5, 7$ and 56: $2, 2, 2, 7$ M1\n- Identifies all factors for LCM (e.g., $2 \\times 2 \\times 2 \\times 5 \\times 7$) M1\n- Final answer: 280 A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Finds prime factors for both 70 and 56.","code":"M"},{"id":"p2","marks":1,"description":"Identifies the correct set of factors to multiply for LCM.","code":"M"},{"id":"p3","marks":1,"description":"Calculates the LCM as 280.","code":"A"}],"finalAnswers":["280"],"generatedAt":"2026-05-07T01:47:16.835Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"prime_factorisation","label":"Prime factorisation","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"$$70=2\\times5\\times7$"},{"latex":"$$56=2\\times2\\times2\\times7$"}]},"order":0,"title":"Factorise each number","description":"Break each number into prime factors. A prime number has exactly two factors: itself and one. These complete prime factorisations earn M1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$70=2\\times \\color{@orange}{\\htmlData{anchor=five}{5}}\\times \\color{@green}{\\htmlData{anchor=seven_a}{7}}$"},{"latex":"$$56=\\color{@sky}{\\htmlData{anchor=twos}{2\\times2\\times2}}\\times \\color{@green}{\\htmlData{anchor=seven_b}{7}}$"},{"latex":"$$\\operatorname{LCM}=\\color{@sky}{2\\times2\\times2}\\times \\color{@orange}{5}\\times \\color{@green}{7}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"twos"},{"color":"orange","style":"text-color","anchor":"five"},{"color":"green","style":"text-color","anchor":"seven_a"},{"color":"green","style":"text-color","anchor":"seven_b"}]},"order":1,"title":"Choose the factors","description":"For the LCM, take each prime the greatest number of times it appears in either factorisation. Identifying all the required factors earns M1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\operatorname{LCM}=\\htmlData{anchor=product}{2\\times2\\times2\\times5\\times7}$"},{"latex":"$$\\operatorname{LCM}=\\color{@green}{\\htmlData{anchor=answer}{280}}$"}],"highlights":[{"color":"green","style":"text-color-with-background","anchor":"answer"}],"connections":[{"to":"answer","from":"product","color":"green","label":"multiply"}]},"order":2,"title":"Multiply the factors","description":"Multiply the selected prime factors to obtain the lowest common multiple. The correct result, 280, earns A1."}]}],"generatedAt":"2026-07-20T16:41:22.137Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":57,"sampleSize":35}},{"id":"e2043536-a44c-4b27-8b58-ab871c63d221","revisionId":"cb6a3e8d-c5e6-46d9-8d44-4b17008a092a","questionNumber":"9","questionType":"LA","specification":"Two buses, bus A and bus B, both use the same bus stop.\n\nBus A runs every 10 minutes.\n\nBus B runs every 14 minutes.\n\nBoth buses are at the bus stop at 11 am.","difficulty":2,"difficultyBand":null,"totalMarks":3,"sourceTitle":"Prime Factors, HCF and LCM","calculatorUse":null,"parts":[{"id":"838f2a72-99ca-4263-9c70-ba91b60abad5","label":"0","content":"What time will both buses next both be at the bus stop.","markscheme":"- Finds LCM of 10 and 14: $10 = 2 \\times 5$, $14 = 2 \\times 7$, $LCM = 2 \\times 5 \\times 7 = 70$ M1\n- Adds 70 minutes to 11 am M1\n- Final answer: 12:10 pm A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Calculates the LCM of 10 and 14 as 70.","code":"M"},{"id":"p2","marks":1,"description":"Adds the LCM (70 minutes) to the start time of 11 am.","code":"M"},{"id":"p3","marks":1,"description":"States the correct time as 12:10 pm.","code":"A"}],"finalAnswers":["12:10 pm","12:10"],"generatedAt":"2026-05-07T01:47:16.835Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"prime_factor_lcm","label":"Prime factors and LCM","steps":[{"type":"text","order":0,"title":"Identify the LCM","content":"The buses will ne

Prime Factors, HCF and LCM Questions

Prime Factors, HCF and LCM Questions

Prime Factors, HCF and LCM Questions

Prime Factors, HCF and LCM Questions