You have basketball practice every fourth day, and soccer practice every 6th day. today you had both practices. in how many days will you have both practices on the same day again?

12 days from now

Explanation:

Below are two lists. The first list has every 4th number in bold. The second list has every 6th number in bold. Basically I'm showing multiples of 4 and 6.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

1, 2, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12

We see that both days are in bold on day 12.

It might help to list out the multiples of 4 and 6 respectively like so

multiples of 4 = {4, 8, 12, 16, 20, 24...}

multiples of 6 = {6, 12, 18, 24, 30, 36...}

The 12's in bold are the lowest common multiple (LCM) between the two lists of multiples. The next common multiple is 24, which is just 12 more than the LCM. Basically any other common multiple will be a multiple of 12.

Common multiples = {12, 24, 36, 48, ...}

A shortcut is to multiply 4 and 6 to get 4*6 = 24. This is a common multiple of 4 and 6, but it is not the smallest. We can divide out the GCF 2

24/2 = 12

So the general formula to find the LCM of x and y is

LCM = (x*y)/G

where G represents the GCF of x and y.

7

step-by-step explanation: