Ángel went to the doctor and was prescribed three different medications: one in capsules, a syrup and some drops. The capsules should be taken every 6 hours, the syrup every 3 hours and the drops every 4 hours. If when Cristóbal starts treatment he takes the three medications at 8:00 am, at what time does he take the three medications together again?

6 = 2 * 3 3 = 3 4 = 2^2 Now, take the highest power of each prime: The highest power of 2 is 2^2 = 4. The highest power of 3 is 3. There are no other prime factors. Now, multiply these highest powers to find the LCM: LCM = 4 * 3 = 12 hours So, Ángel will need to take all three medications together again every 12 hours. If he starts taking them at 8:00 am, the next time he needs to take all three medications will be 12 hours later, which is 8:00 pm.