Learning Target

 Todays learning target was using the prime factorization of composite numbers to find the greatest common factor (GCF), and the least common multiple (LCM).

Example Problem

                              16                                  8

                              /\                                 /\                          

                          8   X  2                        4    x    2

                         /\                                /\

                      4  X  2                          2 X 2

                     /\

                   2 X 2

 2X2X2X2=16                                        2X2X2 = 8

  The GCF (Greatest Common Factor) is eight. This is because each of the numbers has two three times in it ( 2x2x2=8).

  The LCM (Least Common Multiple) is sixteen. You find this by making a list of the multiples for each number:

8:8,16,24,32 and

16:16,32,48 then selecting the lowest number in both lists = 16.

Or you could do a multiplication problem . For this problem it would be 2x2x2x2=16. You do this because it contains all the factors required for making both eight and sixteen.

Lesson

You find the GCf by using prime factorization. First you find all the prime factors for each number.  Then you determine the product of all the prime factors that occur for both numbers.  This product is the GCF.

To find the LCM, you make a list of the first of the first four or five multiples for each number and look for the lowest number that is in both lists.  If you don't find one, do the next five multiples and repeat until you find the same number in each list.  This is the LCM. Or you can use prime factorization. Once you find the prime factors for both numbers the LCM is the product of all the prime factors of both numbers without any repeted factors.

Check out this link:

http://mathworld.wolfram.com/LeastCommonMultiple.html

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Posted by: bucherc    in: My entries

Modified on November 10, 2006 at 10:13 PM