1) A shop has 120 pens and 180 notebooks and wants the biggest equal stationery bundles.  a) HCF of 120 and 180 is 60 (bundles) b) LCM of 120 and 180 is 360 (bundles) 2) A tour company has 48 French-speaking tourists and 60 Spanish-speaking tourists and wants the largest equal groups. a) LCM of 48 and 60 is 240 (groups) b) HCF of 48 and 60 is 12 (groups) 3) Two hotel shuttles leave every 12 minutes and 18 minutes. When do they leave together again? a) LCM of 12 and 18 is 36 (min) b) HCF of 12 and 18 is 6 (minutes) 4) Stage lights cycle every 50 seconds and a bass effect every 75 seconds. When do they activate together? a) LCM of 50 and 75 is 150 (seconds) b) HCF of 50 and 75 is 25 (seconds) 5) An electrician has 90 cm and 150 cm cables and wants to cut them into the longest identical pieces. a) LCM of 90 and 150 is 450 (identical pieces) b) HCF of 90 and 150 is 30 (identical pieces) 6) A shop receives paper every 14 days and ink every 21 days; when do the deliveries match? a) LCM of 14 and 21 is 42 (days) b) HCF of 14 and 21 is 7 (days) 7) A boiler filter is replaced every 40 days and a valve checked every 28 days; when will both jobs fall together? a) LCM of 40 and 28is 280 (days) b) HCF of 40 and 28 is 4 (days) 8) A technician has 72 small speakers and 48 large speakers and wants identical sound kit bundles. a) LCM of 72 and 48 is 144 (bundles) b) HCF of 72 and 48 is 24 (bundles) 9) Circuit A is tested every 30 days and Circuit B every 45 days; when do the tests coincide? a) LCM of 30 and 45 is 90 (days) b) HCF of 30 and 45 is 5m (days) 10) A carpenter has 64 oak planks and 96 pine planks and wants maximum identical furniture kits. a) HCF of 64 and 96 is 32 (kits) b) LCM of 64 and 96 is 192 (kits)

LCM and HCF vocational problems

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