Least Common Multiple
Lesson
Topic Index | Grade 5 Math | Intermediate Test Prep | StudyZone

 

The least common multiple (LCM) of two numbers is the smallest number (not zero) that is a multiple of both.

Review:  A multiple is found by multiplying the given number by 1, by 2, by 3, and so on.

We can find the LCM of two or more numbers by looking at their prime factors.  Use factor trees to find the prime factors.

Take a look at this example...

What is the LCM of 16 and 20?


 

The prime factors of 16 are 2 2 2 2
AND
The prime factors of 20 are 2 2 5

We now multiply each factor the greatest number of times it occurs in either number.

2 occurs four times in the 16
AND
1 occurs once in the 20

SO...

We multiply 2 2 2 2 5 and find
the LCM to be 80.


What if we had three numbers?

What is the LCM of 6, 9, and 12?

                               

The prime factors of 6 are 2 3,

The prime factors of 9 are 3 3,
AND
The prime factors of 12 are 2 2 3

2 occurs two times in the 12
AND
3 occurs two times in the 9

SO...

We multiply 2 2 3 3 and find
the LCM to be 36.

 

Let's Practice