When we learned adding and subtracting fractions, we learned that the number on the bottom, the denominator, has to be the same. In order to get a common denominator, we first need to find the Least Common Multiple (LCM). The LCM of 2 numbers is the smallest number that both numbers divide evenly. The video below will explain 2 methods of finding LCMs:
List the multiples of each of the numbers given and find the smallest number in both lists.
Prime Factorization
Find all the prime factors of each number given.
Create a new number that contains all the prime factors of each number. Remember to include multiples If there are multiples of the same factor in either prime factorization. Example: 9 = 3 × 3 and 15 = 3 × 5, since 9 has two 3s and 15 has only one 3 in its factorization, the combined list will need two 3’s. The LCM of 9 and 15 is 3 × 3 × 5 = 45
To find the least common multiple (LCM) we will start by finding the prime factors of both 4 and 12.
Since 2 is prime, we can write the prime factorization of 4 as 2 × 2.
Since 2 and 3 are both prime, we can write the prime factorization of 12 as 2 × 2 × 3.
So we have
4 = 2 × 2
12 = 2 × 2 × 3
Our LCM will need to have the prime factors of both 4 and 12. Since the prime factorization of 4 is 2 × 2 and the prime factorization of 12 has 2 × 2 in it, we will only need to include 2 × 2 once.
To find the least common multiple (LCM) we will start by finding the prime factors of both 6 and 10.
Since 2 and 3 are both prime, we can write the prime factorization of 6 as 2 × 3.
Since 2 and 5 are both prime, we can write the prime factorization of 10 as 2 × 5.
We have
6 = 2 × 3
10 = 2 × 5
Our LCM will need to have the prime factors of both 6 and 10. Since the prime factorization of both 6 and 10 include a 2, we will only need to include 2 once.
To find the least common multiple (LCM) we will start by finding the prime factors of both 4 and 14.
Since 2 is prime, we can write the prime factorization of 4 as 2 × 2.
Since 2 and 7 are both prime, we can write the prime factorization of 14 as 2 × 7.
We have
4 = 2 × 2
14 = 2 × 7
Our LCM will need to have the prime factors of both 4 and 14. Since the prime factorization of 4 is 2 × 2, when we include the prime factors of 14 we already have at least one 2, so we do not need to include another 2.
To find the least common multiple (LCM), we will start by finding the prime factors of both 7 and 5. Since 7 and 5 are both prime, the prime factorization of each is just itself.
We have
5 = 5
7 = 7
Our LCM will need to have the prime factors of both 7 and 5, so we will include both 7 and 5.
Since 2 and 3 are both prime, we can write the prime factorization of 6 as 2 × 3.
Since 2 is prime, we can write the prime factorization of 4 as 2 × 2.
Since 2 and 3 are both prime, we can write the prime factorization of 12 as 2 × 2 × 3.
Since 2 and 5 are both prime, we can write the prime factorization of 10 as 2 × 5.
Since 2 and 7 are both prime, we can write the prime factorization of 14 as 2 × 7.
Since 3 is prime, we can write the prime factorization of 9 as 3 × 3.
