[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-360725-105":59,"doc-detail-360725-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","least-common-multiple-word-problems-b-track-field","Least Common Multiple Word Problems (B) - Track & Field","","Least Common Multiple Word Problems (B) - Track & Field provides eight step-by-step least common multiple challenges using real-world athletic scenarios. Students solve problems involving runners’ lap times, whistle schedules, rotating track events, stadium heat timing, and ordering intervals for equipment. Each item requires finding the next time multiple cycles align and often counting how many times each event occurs by that moment. An answer key confirms solutions and includes brief factor-based reasoning for each least common multiple.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/least-common-multiple-word-problems-b-track-field/360725/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/least-common-multiple-word-problems-b-track-field/360725.png","ImageObject",300,407,{"name":92,"@type":93},"Aditya","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-24","2026-09-23",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do you find when two runners are both back at the starting line?","Question",{"text":113,"@type":114},"Compute the least common multiple of their lap intervals and convert that result into minutes. The LCM gives the first time both return together.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How do you determine when multiple events start at the same time again?",{"text":118,"@type":114},"Find the least common multiple of the event intervals (e.g., hurdles and relay, or three rotating events). Use the LCM to identify the next shared start time and the required counts.",{"name":120,"@type":111,"acceptedAnswer":121},"What does the answer key include for each problem?",{"text":122,"@type":114},"Each entry lists the final answer and short steps showing how the LCM is formed from prime factors, followed by counts of how many times each event or order occurs by the aligned day or time.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},360725,1790871462,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":52,"preview_page_count":4},962085564549,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","Name:     \nLeast Common Multiple Word Problems (B)  \nTRACK & FIELD  \nDirections: Solve each word problem. Show all of your work.  \n1. Runner A completes a lap every 3 minutes and Runner B completes a lap every 5 minutes. If both start at the same time, after how many minutes will they both be at the starting line at the sametime? Show your work:  \n2. A coach blows a whistle every 8 minutes for sprinters and every 12 minutes for distance runners. If both whistles are blown at the start, after how many minutes will both be blown at the same time again? Show your work:  \n3. At a track meet, the hurdles race starts every 10 minutes and the relay race every 15 minutes. Both events start at noon. At what time will both events next start at the same time? How many hurdles races will have started by then?  \nShow your work:  \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)  \n4. Three runners train on the same track. Runner 1 completes a lap every 4 minutes, Runner 2 every  \n6 minutes, and Runner 3 every 9 minutes. If all start together, after how many minutes will all three be at the starting line at the same time?  \nShow your work:  \n5. A stadium fires a starter pistol every 6 minutes for sprint heats, every 10 minutes for middledistance heats, and every 15 minutes for long-distance heats. All events start at the same time. After how many minutes will all three events start simultaneously again?  \nShow your work:  \n6. A school orders new hurdles every 16 days and new relay batons every 20 days. Both are ordered on the same day. After how many days will both items next be ordered on the same day? How many orders of each item will have been placed by then?  \nShow  \nyour work:  \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)  \n7. Athlete A does a strength workout every 14 days and Athlete B does one every 21 days. Both complete a workout on Day 1. What is the next day both will work out on the same day? How many workouts will each have completed by then (including Day 1)?  \nShow your work:  \nChallenge Problem  \n8. Three track events rotate through a stadium: the 100m sprint every 12 days, the 400m race every  \n18 days, and the 1500m race every 30 days. All three are held on Day 1. What is the next day all three will be held on the same day? How many times will each event have been held by then (including Day 1)?  \nShow your work:  \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)  \nANSWER KEY  \n1.) 1. ) Answer: 15 minutes Steps: 3 and 5 share no common factors → LCM(3,5) = 3×5 = 15 minutes  \n2.) 2. ) Answer: 24 minutes Steps: 8 = 2³ 12 = 2² ×3 → LCM(8,12) = 2³ ×3 = 24 minutes  \n3.) 3. ) Answer: 12:30 p.m.; 3 hurdles races Steps: LCM(10,15): 10=2×5, 15=3×5 → LCM=2×3×5=30 minutes → 30 minutes after noon = 12:30 p. m. → Hurdles: 30÷10 = 3 races  \n4.) 4. ) Answer: 36 minutes Steps: LCM(4,6): 4=2² , 6=2×3 → LCM=2² ×3=12 → LCM(12,9): 9=3² → LCM=2² ×3²=36 minutes  \n5.) 5. ) Answer: 30 minutes Steps: LCM(6,10): 6=2×3, 10=2×5 → LCM=2×3×5=30 → LCM(30,15):  \n15=3×5 → LCM=30 minutes  \n6.) 6. ) Answer: Day 80; hurdles: 5 orders, batons: 4 orders Steps: 16 = 2⁴ 20 = 2² ×5 → LCM(16,20)= 2⁴ ×5 = 80 days → Hurdles: 80÷16 = 5 orders Batons: 80÷20 = 4 orders  \n7.) 7. ) Answer: Day 42; Athlete A: 3 workouts, Athlete B: 2 workouts Steps: 14 = 2×7 21 = 3×7 → LCM(14,21) = 2×3×7 = 42 → Next shared day: Day 42 → Athlete A: 42÷14 = 3 workouts Athlete B: 42÷21 = 2 workouts  \n8.) 8. ) Answer: Day 180; 100m: 15 times, 400m: 10 times, 1500m: 6 times Steps: LCM(12,18):  \n12=2² ×3, 18=2×3² → LCM=2² ×3²=36 → LCM(36,30): 30=2×3×5 → LCM=2² ×3² ×5=180 → 100m: 180÷12=15 400m: 180÷18=10 1500m: 180÷30=6  \nMashup Math LLC | Al","cbCail2u2bjSXjIG","https://ap.wps.com/l/cbCail2u2bjSXjIG","pdf",520220,"English","# Least Common Multiple Word Problems (B)\n## Directions\n## Problems 1-3\n## Problems 4-6\n## Problems 7-8\n## Answer Key","[{\"question\":\"How do you find when two runners are both back at the starting line?\",\"answer\":\"Compute the least common multiple of their lap intervals and convert that result into minutes. The LCM gives the first time both return together.\"},{\"question\":\"How do you determine when multiple events start at the same time again?\",\"answer\":\"Find the least common multiple of the event intervals (e.g., hurdles and relay, or three rotating events). Use the LCM to identify the next shared start time and the required counts.\"},{\"question\":\"What does the answer key include for each problem?\",\"answer\":\"Each entry lists the final answer and short steps showing how the LCM is formed from prime factors, followed by counts of how many times each event or order occurs by the aligned day or time.\"}]","Least Common Multiple Word Problems (B) - Track & Field | PDF",1790141342]