Question

Question #7b8e2

Answer 1

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 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