# Question #7b8e2

##### 1 Answer

Here is a common way to do so:

Factorize each number into its prime factorization

Pick a prime factor and find the number out of the three which has the most of that prime factor

Write down (in a separate list) whichever prime factor you chose that many times

Repeat steps 2 and 3 until there aren't any factors left

Multiply together all of the factors in your list to get the LCM

**Example:**

Let's find the LCM of

*Step 1:*

The prime factorization of 18 is

#2 xx 3 xx 3#

The prime factorization of 45 is#3 xx 3 xx 5#

The prime factorization of 84 is#2 xx 2 xx 3 xx 7#

*Step 2:*

Let's start with 2. The most

#2# 's that any number has is#2# (84 has 2), so let's add#2# #2# 's to our list:

*Step 3.*

List:

#2, 2#

*Step 4.*

Let's do 3 next. The most

#3# 's that any number has is#2# (18 and 45 both have 2), so let's add#2# #3# 's to our list:List:

#2, 2, 3, 3# Next is 5. The only number that has a

#5# is 45, and it has one#5# , so let's add one#5# to our list.List:

#2, 2, 3, 3, 5# Finally, we're left with 7. The only number that has a

#7# is#84# , and it has one#7# , so let's add one#7# to our list.List:

#2, 2, 3, 3, 5, 7# This is our complete list!

*Step 5.*

#"LCM" = 2 xx 2 xx 3 xx 3 xx 5 xx 7 = 1260#

*Final Answer*