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Lupita and Vin both swam in the indoor pool at the same gym today. Lup

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Lupita and Vin both swam in the indoor pool at the same gym today. Lup  [#permalink]

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New post 22 Mar 2018, 23:37
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Lupita and Vin both swam in the indoor pool at the same gym today. Lupita swims at that gym every 12 days. Vin swims there every 15 days. If both continue with their regular swimming schedules at the gym, the next time both will swim there on the same day is in how many days?

(A) 12
(B) 15
(C) 30
(D) 45
(E) 60

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Re: Lupita and Vin both swam in the indoor pool at the same gym today. Lup  [#permalink]

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New post 23 Mar 2018, 00:15
Bunuel wrote:
Lupita and Vin both swam in the indoor pool at the same gym today. Lupita swims at that gym every 12 days. Vin swims there every 15 days. If both continue with their regular swimming schedules at the gym, the next time both will swim there on the same day is in how many days?

(A) 12
(B) 15
(C) 30
(D) 45
(E) 60


LCM of 12 and 15

60
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Lupita and Vin both swam in the indoor pool at the same gym today. Lup  [#permalink]

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New post 23 Mar 2018, 00:16
Bunuel wrote:
Lupita and Vin both swam in the indoor pool at the same gym today. Lupita swims at that gym every 12 days. Vin swims there every 15 days. If both continue with their regular swimming schedules at the gym, the next time both will swim there on the same day is in how many days?

(A) 12
(B) 15
(C) 30
(D) 45
(E) 60


Lupita swims in the indoor pool once every 12 days.
Lupita will swim in the pool during the 12th,24th,36th,48th, and 60th day.
Vin swims in the indoor pool once every 15 days.
Vin will swim in the pool during the 15th,30th,45th, and 60th day.

Therefore, the day the two of them swim on the same day is the 60th day(Option E)

P.S the underlying principle for problems like this is to find the LCM
of the two numbers. Here LCM(\(12 = 2^2*3,15 = 3*5\)) is\(2*2*3*5 = 60\)
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Lupita and Vin both swam in the indoor pool at the same gym today. Lup &nbs [#permalink] 23 Mar 2018, 00:16
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