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So, what are you learning in math? We’re trying to find Least Common Multiple and Greatest Common Factor. They must be really lost…people have been looking for them since I was a child. • A prime number is a natural number that has exactly two positive factors, 1 and itself. • A composite number is a natural number that has more than two positive factors. • (Now might be a good time to review divisibility rules.) • 0 is neither prime nor composite because it is not a natural number. • 1 is neither prime nor composite because it only has one factor, 1. Hut two! Hut three! Hut Five! Seven! Eleven! 13! 17! 19! 23! 29!.... And Deion Sanders thought HE was Prime Time! See video • Prime factorization is a number written as a product of all its prime factors. • You can use factor trees to find the prime factorization of a number. – You might have different branches than someone else, but you should end up with the same prime numbers on the bottom of all branches. – Let’s look at two ways to find the prime factorization of the number 12. 12 = 2 x 2 x 3 = 22 x 3 12 6 3 2 2 12 3 3 4 2 2 See video • The greatest common factor is the largest factor that two or more numbers have in common. • You might remember the listing method to find the greatest common factor, GCF. factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 factors of 54: 1, 2, 3, 6, 9, 18, 27, 54 GCF(36,54) = 18 • You can also use prime factorization. (GCF is the product of all prime factors the numbers have in common) 36 = 2 x 2 x 3 x 3 54 = 2 x 3 x 3 x 3 GCF(36,54) = 2 x 3 x 3 = 18 See video • The least common multiple is the smallest natural number that is a common multiple of two or more numbers . • You might remember the listing method to find the least common multiple, LCM. 0 is a multiple of multiples of 36: 0 , 36, 72, 108 , 144 , 180but , …LCM each, needs be > 0. , … multiples of 26: 0 , 26, 52 , 78, 104 , 130to , 156 , 182 …but it’s not always the easiest method. You can also use prime factorization. (Multiply all prime factors but don’t include factors you already listed from a different number.) 26 = 2 x 13 36 = 2 x 2 x 3 x 3 LCM(26,36) = 2 x 13 x 2 x 3 x 3 = 26 x 18 = 468 Practice • Here is a great website to practice making factor trees. If you ask for two trees, you will be asked to find GCF and LCM after finding the prime factors. You can even select to pick the numbers yourself. • Enjoy!