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Cristobal went to the doctor and was prescribed three different medications: one in capsule form, a syrup, and some drops. He must take the capsules every 4 hours, the syrup every 2 hours, and the drops every 5 hours. If Cristobal starts the treatment and takes the three medications at 8:00 a.m., at what time does he take them all together again?

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Answer to a math question Cristobal went to the doctor and was prescribed three different medications: one in capsule form, a syrup, and some drops. He must take the capsules every 4 hours, the syrup every 2 hours, and the drops every 5 hours. If Cristobal starts the treatment and takes the three medications at 8:00 a.m., at what time does he take them all together again?

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Cristian
4.7
119 Answers
\text{First, find the least common multiple (LCM) of the medication intervals:}

\text{Capsules: every 4 hours}

\text{Syrup: every 2 hours}

\text{Drops: every 5 hours}

\text{The LCM of 4, 2, and 5:}

\text{Prime factorizations:}

4 = 2^2

2 = 2

5 = 5

\text{LCM is determined by the highest power of each prime number:}

\text{LCM} = 2^2 \cdot 5 = 4 \cdot 5 = 20 \text{ hours}

\text{Since he takes the medications at 8:00 am, add 20 hours:}

8:00am-4hours=4:00am

\text{The answer is 4:00 am}

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