# Question #7b8e2

Oct 17, 2017

Here is a common way to do so:

1. Factorize each number into its prime factorization

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

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

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

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

Example:

Let's find the LCM of $18$, $45$, and $84$

Step 1:

The prime factorization of 18 is $2 \times 3 \times 3$
The prime factorization of 45 is $3 \times 3 \times 5$
The prime factorization of 84 is $2 \times 2 \times 3 \times 7$

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.

$\text{LCM} = 2 \times 2 \times 3 \times 3 \times 5 \times 7 = 1260$