I have gymnastics practice very 3 days and tennis practice every 8 days. How many days will it take for me to have BOTH gymnastics and tennis practice on the same day?​

24 days

Step-by-step explanation:

Find LCM, or least common multiple

List out all the multiples of 3:

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, ...

Now 8:

8, 16, 24, 32, 40, 48, 56, 63, 72, 80, 88...

LCM is 24, because they both hit 24 first.

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Explanation:

This is because 24 is the LCM (lowest common multiple) of 8 and 3.

We multiply the given values to get 8*3 = 24. This trick only works if the original two numbers have no common factors other than 1.

We can verify that 24 is indeed the LCM by listing out the multiples

We see that 24 is found in both lists and it's the smallest such item. The next common item would be 48, which is a multiple of 24. In other words, every 24 days, your two practices will line up on the same day.