What is the lcm of 12 and 18

36

Step-by-step explanation:

Hi there!

We want to find the least common multiple (LCM) of 12 and 18

One easy way to do that is to split up the numbers into one of their factor pairs, find the factor pairs between the numbers we just split apart, and then keep on going, until we only get prime numbers (numbers that only have 1 and itself as multiples)
Let's start with 12.

There are multiple ways to multiply to get to 12, but we can use 3 and 4 for example

12= 3*4

4 is 2 * 2  

Substituting 2*2 for 4, 12 is equal to 2*2*3

Now for 18.

18 can also be split up multiple ways; one way would be 9 and 2

18 = 2*9

9 is 3*3

Substitute 3*3 for 9.

18=2*3*3
Now look at 2*2*3; 2 shows up twice in that string of numbers

In 2*3*3, 3 shows up twice in that string of numbers

We multiply the numbers based off of the highest number of times that they occur
In other words, we will multiply 2 * 2  and 3 * 3 together
2 * 2 * 3 * 3 = 4 * 9 = 36
The LCM of 12 and 18 is 36

Hope this helps!

See more on finding the LCM here:

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