Goal:
Goal:
Another strategy you can use to find the LCM is prime factorization. Recall that the prime factorization of a number is when a number is factored using only prime numbers. Note that each number has a unique prime factorization.
Find the least common multiple of 15 and 25 using prime factorization.
Review the slides to see how to find the LCM of 15 and 25 using prime factorization.
To start, you need to know the prime factorization of each number you are working with. One way to do this is by making a factor tree for each number.
Prime factorization of 15:
The prime factorization of 15 is 3 x 5.
Prime factorization of 25:
The prime factorization of 25 is 5 x 5.
Neatly line up the prime factorization of each number so that like terms are in the same columns.
Notice that the like factors are neatly lined up in vertical columns. There are no 3s in the prime factorization of 25, so there should not be a number lined up with 3.
Now that you have neatly lined up your factors, you can easily compare them.
The prime factorizations of 15 and 25 share one 5.
To find the LCM you will list one factor from each column of your prime factorization. Like this:
Then multiply the factors: 3 x 5 x 5 = 75.
The least common multiple of 15 and 25 is 75.
15 x 5 = 75
25 x 3 = 75
Your turn! Practice using prime factorization to find the LCM of the number sets below. When you have finished, click the box to check your answers.
