1. Carol Chervenak Finding the Greatest Common Factor (GCF) and the Least Common Multiple (LCM) using Prime Factorization! No need to make lists like you used to :-)

2. Factor: One number is a factor of another if it divides that number with NO remainder. Example: The factors of 10 are 1, 2, 5, 10. Greatest Common Factor: (GCF) The greatest common factor of two or more numbers is the greatest number that is a factor of all the numbers. Example: The GCF of 6 and 8 is 2. Definitions

3. Multiple: A multiple of a number is the product of that number and any nonzero whole number. 48 is a multiple of 8 because 8 x 6 = 48. Least Common Multiple: (LCM) The least common number that is a common multiple of two or more numbers is the least common multiple. The LCM of 8 and 12 is 24.

4. You can use a Venn Diagram to find the GCF and LCM of 2 or more numbers. WONDERING HOW?

5. Find the Greatest Common Factor of 64 and 120. Then find the Least Common Multiple of the same two numbers. Start by finding the prime factorization of each number. (Factor trees will help if you can’t do it in your head.) 64= 120= 2x2x2x2x2x2 2x2x2x3x5 Y ou may not want to use exponents in these prime factorizations.

6. 64= 222222120= 22235 64120 Common factors go here. 2 2 2 2 2 2 3 5 The GCF = 8 because the common prime factors are 222. Go to the next slide to find the LCM!

7. 64= 222222120= 22235 64120 Common factors go here. 2 2 2 2 2 2 3 5 To find the LCM, multiply the prime factors. 22222235 The LCM of 64 and 120 = 960.

8. Try this!! Find the GCF and the LCM of 75 and 60. First find both prime factorizations. 75=60= LCM of 75 and 60 =GCF of 75 and 60 = Go to the next slide to see if you’re correct!

9. Try this!! Find the GCF and the LCM of 75 and 60. First find both prime factorizations. 75=60= LCM of 75 and 60 =GCF of 75 and 60 = 2235355 3 5 5 2 2 300 15

10. Using a Venn Diagram is just one way to find the GCF and LCM. There’s no need to make those long lists of factors and multiples once you practice this. This method is good to use if you can do prime factorizations well!