NF - Greatest Common Factor (GCF) and Least Common Multiple (LCM) Lesson

Math_Lesson_TopBanner.png Greatest Common Factor (GCF) and Least Common Multiple (LCM)

Now we're going to use what we learned about factors to find the Greatest Common Factor and Least Common Multiple . A common factor is a number that is a factor of two or more numbers.

What is the Greatest Common Factor? (GCF)

The greatest common factor (GCF) is the largest number that divides evenly into the given numbers.

Here's an example.

  • What's the GCF of 12 and 24?
  • We're looking for the largest number that divides evenly into 12 and 24.
  • In this case it would be 12.

We will show you how to use factor trees to figure this out for larger numbers where the answer is not so easy to find.

What is the Least Common Multiple? (LCM)

The least common multiple (LCM) is the smallest number that is a multiple of the given numbers.

Let's look at an example.

  • Say we are looking at the numbers 2 and 3.
  • Let's list some multiples of each:
    • Multiples of 2: 2, 4, 6, 8, 10
    • Multiples of 3: 3, 6, 9, 12, 15
  • The smallest number that is a multiple of both 2 and 3 is 6.
  • Therefore, the LCM of 2 and 3 is the number 6.

Now let's take a closer look at GCF and LCM.

Question: What two numbers are NEITHER prime nor composite?

Answer: 0 and 1

Let's walk through some examples!

NOTE: For the following examples, the answers don't work correctly when it gets to problems 1-3. You can find those answers below the video.

Problem 1's Answer: Prime Factorization of 11 is 1x11

Problem 2's Answer: Prime Factorization of 9 is 3x3

Problem 3's Answer: Prime Factorization of 45 is 3x3x5

GCF and LCM Word Problems Video

Click HERE Links to an external site. to learn more about solving word problems.

Math_MS6BottomBanner.png

IMAGES CREATED BY GAVS