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Exploring GCF and LCM Methods

Learn how to find GCF and LCM using the ladder and list methods. Discover the concepts of common multiples and least common multiple with engaging activities.

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Exploring GCF and LCM Methods

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  1. Using the ladder method, find the GCF of these numbers: Warm Up 36 48 24 30 30 45

  2. What am I Learning Today? LCM How will I show that I learned it? Use multiples to uncover hidden picture Determine the GCF and LCM using the list and ladder method

  3. Vocabulary Common multiple: multiples shared by two or more whole numbers. Least Common Multiple (LCM): The smallest nonzero number that is a multiple of two or more numbers.

  4. What is the least common multiple? The smallest number that is a multiple of two or more numbers How do I find the LCM? Using the list method or the ladder How do I use the list method? 1. List all the multiples for those two numbers. 2. Circle the smallest multiple that they share. List the LCM for 5 and 8. 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, . . 8: 8, 16, 24, 32, 40, 48, . . . LCM: 40 How do I use the ladder method? • Begin with a factor that divides into each number evenly. • Keep dividing until there are no more common factors. • 3. Find the product of all of the numbers on the outside of the ladder (LCM is ALL OF THEM).

  5. Using the ladder, find the LCM for 40 and 16. 2 40 16 2• 2•2•2• 5 = 80 2 20 8 2 10 4 5 2 What happens if I have two numbers that do not have a common factor other then one? Simply multiply the two numbers together and that IS the LCM “GCF is on the left LCM is all of them”

  6. Find the Least Common Multiple Use BOTH the list and ladder method in order to check your answers. Multiples of 32: 32, 64, 96, 128, 160 Multiples of 24: 24, 48, 72, 96, 120 LCM of 32 and 24 32 24 2 16 12 2 8 6 2 4 3 LCM of 54 and 36 54 36 2 Multiples of 54: 54, 108, 113, 216 Multiples of 36: 36, 72, 108, 144 27 18 3 9 6 3 3 2 “GCF is on the left LCM is all of them”

  7. Find the GCF AND LCM of 30 and 40 2 30 40 5 15 20 34 GCF LCM 2• 5•3• 4= 2• 5= 120 10 “GCF is on the left LCM is all of them”

  8. Find LCM using a Venn Diagram

  9. Paired Discussion Turn to a partner and discuss the following: Why can’t you find the Greatest Common Multiple for a group of numbers? Can the LCM of a set of numbers ever be smaller than any of the numbers in the set? Explain. Multiples go on indefinitely, so there is no possible way to find the GREATEST common multiple. No. It can be equal to one of the numbers, but never smaller. Multiples are products and the smallest one is the identity property which is unique to each number.

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