Answered

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You have diving lessons every fifth day and swimming lessons every third day.today you have both lessons. In how many days will you have both lessons on the same day again?

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It will take 15 days for driving lessons and swimming lessons to end up on the same day again. Since 15 divided by 3 is 5 and 15 divided by 5 is 3, it's the first number which is a multiple of each smaller numbers.
The correct answer is:

In 15 more days.

Explanation:

Diving lessons are every 5 days and swimming lessons are every 3 days.  Both will happen on the day that is the least common multiple, or LCM, of the numbers.

To find the LCM of both numbers, we first find the prime factorization of each:
5 = 1*5

3 = 1*3

The LCM is the common factors multiplied by the uncommon factors.  The common factor is 1.  The uncommon factors are 3 and 5.  This gives us:

LCM = 1*3*5 = 15

This means that today is day 15, since you have both lessons today.  It also means that it will be another 15 days before you have both lessons on the same day again.
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