Question

You have piano lessons every 4th day and guitar lessons every 6th day. Today you have both lessons. In how many days will you have both lessons on the same day again? Explain?

Answer 1

12 because the Least Common Multiple of 6 and 4 is 12 6,12,18,24 4,8,12,16,20

Answer 2

`<b><u>Listing Method</u></b>`

Here, we list some few multiples of 4 and 6.


`image`

Next, we list the common multiples,


`image`

Then we pick the least common multiple which is 12.


`<b><u>Prime Factorization Method</u></b>`

Here we express 4 and 6 as product of prime factors,


`4 = 2 * 2 = {2}^(2) \\ \\ 6 = 2 * 3`

Next, we multiply the common factors with the highest degrees.


`LCM = {2}^(2) * 3 = 4 * 3 = 12`