# LCM & GCF Examples

### Example 1

 Method 1 involves listing the multiples of each number, starting with the number times 1, then times 2, then times 3, and so on.  When you find a multiple that both numbers share, you have found your least common multiple. Find the least common multiple of  and .

### Example 2

 Find the least common multiple of  and .

### Example 3

 The second method for finding the LCM is a little more complicated, but can take less time. To find the LCM, list the prime factors of both numbers. Then count the number of times each prime factor appears for each number. Multiply all prime factors using the greatest number of times it appears in either number. Check out the examples below, as it's easiest to grasp this method by seeing examples. Find the least common multiple of  and .

### Example 4

 Find the least common multiple of  and .

### Example 5

 Method 1 for finding the greatest common factor starts with listing the prime factors for both numbers. Multiply all prime factors that both numbers have in common. Be sure to include a prime factor as many times as it appears in both numbers.Find the greatest common factor of  and .

### Example 6

 Find the greatest common factor of  and .

### Example 7

 Method 2 for finding the GCF is simpler to remember, but can take more time and can lead to more mistakes, since it is easy to forget factors. To find the GCF, list all the factors of each number, not just the prime factors. It can be helpful to write these factors in pairs. Compare the factors of each number until you find the largest one that they both share.Find the greatest common factor of  and .

### Example 8

 Find the greatest common factor of  and .

### Example 9

 You and your dad go grocery shopping. The chocolatey Shmiff Bars that you and your three sisters like come in packages of six. How many packages should your dad buy to make sure that all four of you get an equal number of bars?

### Example 10

 You are getting party favors ready for your little sister's birthday party. There are 24 lollipops, 32 stickers, and 16 mini toys. Assume that you want to use all the prizes (i.e., you don't wants any prizes left over after filling the bags). How many gift bags can you make so that there is an equal number of each prize in each bag and how many prizes will be in each bag?