The Greatest Common Factor of a number is a number that is a factor of both a and b, while the least common multiple is the smallest number that is a multiple of both a and b.
So, let's find the GCF & LCM of (6,24)
to find the GCF, first we have to find the factors of each number. We can do this in a variety of ways. First, we can use the "List Factors" method.
Factors of 6: 1, 2,3 , 6
Factors of 24: 1,2,3,4,6,8,12, 24
We then list the factors both numbers have in common: 1, 2, 3, and 6 Since 6 is the greatest number, 6 is the greatest common factor of 6 and 24.
Another way to do this is by using cuisenaire rods or another linear model. We represent each factor by using colored rods, and determine which is the largest rod in both numbers that is the same color. http://webcache.googleusercontent.com/search?q=cache:JGWSHn386nsJ:www.cerritos.edu/mnikdel/Folder%2520for%2520Word%2520files/Cuisenaire%2520Rods.doc+greatest+common+factor+using+cuisenaire+rods&cd=1&hl=en&ct=clnk&gl=us
This website is a very good visual representation of the method, and also explains how to use it.
We can also use prime factorization again, along with venn diagrams.
Prime Factorization of 6: 2x3
Prime Factorization of 24: 2x2x2x3
Then we draw a venn diagram and write the numbers in the circles based on how many times they appear in either or both numbers. http://www.learner.org/courses/learningmath/number/session6/part_a/index.html
The same methods can be applied to finding the Least Common Multiple, but by substituting multiples for factors.
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