*10:00 am**\n- 2nd flash: $10:00 + 15\\text{ mins} =$ **10:15 am**\n- 3rd flash: $10:15 + 15\\text{ mins} =$ **10:30 am**\n- 4th flash: $10:30 + 15\\text{ mins} =$ **10:45 am**\n- 5th flash: $10:45 + 15\\text{ mins} =$ **11:00 am**\n- 6th flash: $11:00 + 15\\text{ mins} =$ **11:15 am**\n- 7th flash: $11:15 + 15\\text{ mins} =$ **11:30 am**"},{"type":"text","order":2,"title":"List times for Beam B","content":"Now, let's list the flashing times for **Beam B** by repeatedly adding $18$ minutes starting from 9:45 am:\n\n- Start: **9:45 am**\n- 1st subsequent flash: $9:45 + 18\\text{ mins} =$ **10:03 am**\n- 2nd flash: $10:03 + 18\\text{ mins} =$ **10:21 am**\n- 3rd flash: $10:21 + 18\\text{ mins} =$ **10:39 am**\n- 4th flash: $10:39 + 18\\text{ mins} =$ **10:57 am**\n- 5th flash: $10:57 + 18\\text{ mins} =$ **11:15 am**\n- 6th flash: $11:15 + 18\\text{ mins} =$ **11:33 am**"},{"type":"text","order":3,"title":"Identify the common time","content":"By comparing both lists, we look for the first matching clock time after 9:45 am:\n\n- **Beam A times:** 10:00 am, 10:15 am, 10:30 am, 10:45 am, 11:00 am, 11:15 am, 11:30 am...\n- **Beam B times:** 10:03 am, 10:21 am, 10:39 am, 10:57 am, 11:15 am, 11:33 am...\n\nThe earliest matching clock time in both lists is **11:15 am**."},{"type":"text","order":4,"title":"Final Answer","content":"Therefore, both beams will next flash together at **11:15 am**."}]}],"generatedAt":"2026-06-12T10:44:15.124Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":{"percent":45},"walkthroughVideo":{"url":"https://assets.mathsgenie.co.uk/walkthroughs/videos/19cecba1-8bfe-417d-89e8-bdfb41acda6c.mp4","durationSeconds":85,"posterUrl":"https://assets.mathsgenie.co.uk/walkthroughs/videos/19cecba1-8bfe-417d-89e8-bdfb41acda6c.jpg"}},{"id":"4873c05a-a024-4ba1-adce-010a214886de","revisionId":"dac161d1-ddfb-4d00-8fca-64b851f2d712","questionNumber":null,"questionType":"LA","specification":"","difficulty":3,"difficultyBand":"hard","totalMarks":3,"sourceTitle":null,"calculatorUse":"non_calc","isCalculation":true,"parts":[{"id":"9e095a42-c20c-4744-aca3-ede77462690d","label":"a","content":"Bus **A** leaves a station every 8 minutes. \nBus **B** leaves the station every 10 minutes. \nBus **C** leaves the station every 12 minutes.\n\nAll three buses leave the station at the same time.\n\nWork out how long it will take for all three buses to leave the station at the same time again.","markscheme":"- Finding LCM of 8, 10, and 12: $2^3$, $2 \\times 5$, $2^2 \\times 3$ or lists multiples including at least two for each number M1\n- $LCM = 2^3 \\times 3 \\times 5$ (or equivalent calculation or 120 seen) M1\n- Final answer 120 minutes A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Evidence of prime factorization or listing multiples to find the LCM.","code":"M"},{"id":"p2","marks":1,"description":"Correct method to calculate the LCM of all three numbers (e.g., $2^3 \\times 3 \\times 5$).","code":"M"},{"id":"p3","marks":1,"description":"Final correct answer of 120 minutes.","code":"A"}],"finalAnswers":[],"generatedAt":"2026-05-06T14:00:49.522Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"prime_factorisation","label":"Prime factorisation","steps":[{"type":"text","order":0,"title":"Choose the LCM","content":"The buses repeat every $8$, $10$ and $12$ minutes. We therefore need the **lowest common multiple (LCM)**: the smallest positive time that is a multiple of all three intervals.","highlights":[{"text":"all three buses to leave the station at the same time again","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$8=\\color{@sky}{\\htmlData{anchor=eight}{2^3}}$"},{"latex":"$$10=\\color{@amber}{\\htmlData{anchor=ten}{2\\times5}}$"},{"latex":"$$12=\\color{@green}{\\htmlData{anchor=twelve}{2^2\\times3}}$"}],"highl

Prime Factors, HCF and LCM

Question 2

Prime Factors, HCF and LCM Questions

Prime Factors, HCF and LCM

Question 2

Prime Factors, HCF and LCM Questions