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Today's Goal: Today by the end of class you will be able to identify and find Greatest Common Factors and Least Common Multiples. In addition, you will be able to decide which one (GCF or LCM) is appropriate in a given situation.
Greatest Common Factor (GCF)
The first method is using factor trees.
1. First create factor trees for each number you wish to find the common factor for. For our example we will use 12 and 18.
Least Common Multiple (LCM)
Tutorial: Good explanation of LCM and some practice.
There are two methods for finding the Least Common Multiple (LCM).
#1 - Skip Counting.
1. In the first method make a list of several multiples of each numbers.
2. Find which numbers (multiples) they have in common.
3. Locate the lowest of these common multiples, that is the LCM.
2. Once the factor tress are done for each number, let's find the factor they have in common.
3. We see that the that 12 & 18 have 2 and 3 as common factors.
This method can be used with more than two numbers as well.
4. Multiply together all common factors, in this case 2 • 3
5. This gives us our greatest common factor. The GCF is 6
The second method is called the ladder method, upside down birthday cake or Lola May.
1. Using the Lola May method, write the two numbers being factored side by side.
2. Draw an L shaped line around these numbers.
3. Look at the two numbers and come up with a number (factor) that can divide into both numbers. It must be common, but it does not have to be the greatest common factor.
4. Write this number to the left of the L you drew.
5. Now divide each number by this common factor writing the quotient (answer) underneath the number and on the other side of the L you drew.
Method #2 - Lola May
We have discussed the Lola May method before. This is an effective method in that once done it provides the Greatest Common Factor (GCF), the Least Common Multiple (LCM) and it will also reduce fractions to lowest terms.
Videos:
LCM - List Method
Practice Sites for LCM
Snowball Fight - Find the LCM and throw he snowball. Don't get it wrong or they throw one at you.
LCM Matching - Match the LCM with its factors.
Review sites - Reviews LCM, GCF, and Prime factors.
Jeopardy - Play by yourself or with a friend.
6. Now draw another L.
7. Repeat the process until there are no more common factors.
8. Look at the numbers that you divided by that are now listed on the left side of the ladder. Circle them if you want. These are your common factors.
9. To find the greatest common factor you have to multiply all these numbers together. The product is your GCF.
Practice Sites for GCF
Fruit Shoot - Shoot the fruit that contains the greatest common factor. Start at level pone and work your way up.
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