A patient is prescribed three medicines: one every 5 hours, one every 8 hours and one every 20 hours. All three are taken together at 6 a.m. on Monday.
When will all three next be taken together?

LCM(5, 8, 20) = $2^3\times$ 5 = 40 hours. From 6 a.m. Monday, 24 hours reaches 6 a.m. Tuesday and 16 hours more reaches 10 p.m. on Tuesday. Adding the intervals (5 + 8 + 20 = 33 h) wrongly gives 3 p.m. on Tuesday; doubling the LCM to 80 h gives 2 p.m. on Thursday; using the HCF of 1 hour gives 7 a.m. on Monday.