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Greatest Common Factor (GCF) and Least Common Multiple (LCM)

Greatest Common Factor (GCF) and Least Common Multiple (LCM). What is a factor?. A factor is a number that is multiplied by another number to find a product. Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. What is a multiple?.

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Greatest Common Factor (GCF) and Least Common Multiple (LCM)

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  1. Greatest Common Factor (GCF) and Least Common Multiple (LCM)

  2. What is a factor? A factor is a number that is multiplied by another number to find a product. Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

  3. What is a multiple? A multiple is the product of a given number and another number. Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48 Multiples of 10: 10, 20, 30, 40, 50, 60…

  4. Greatest Common Factor The greatest factor that two or more numbers have in common. Example: 45: 1, 3, 5, 9, 15, 45 27: 1, 3, 9, 27 9 is the greatest factor 45 and 27 have in common so GCF= 9

  5. Least Common Multiple The smallest number that is a common multiple of two or more numbers. Example: 12: 12, 24, 36, 48, 60, 72, 84 8: 8, 16, 24, 32, 48, 56 24 is the smallest common multiple so LCM= 24

  6. A New Method First, draw a sideways L on your paper. It will look like an upside down division line. ¬

  7. Greatest Common Factor Greatest Common Factor Place the two numbers you are comparing INSIDE the L. Leave a space in between the numbers. 6 12

  8. Greatest Common Factor Greatest Common Factor Choose a prime number that can divide both numbers. For example, 6 and 12 are both divisible by 3. Place the 3 to the LEFT, just outside of the L. 3 6 12

  9. Greatest Common Factor Divide the pair of numbers by the prime number and write the answers underneath the L. Underneath the 6, for example, you would have a 2 and underneath the 12, you would have 4. The 2 and the 4 can still be reduced, so draw another L to surround them. Place another prime number on the outside of the L and divide again. You can stop now since you have only prime numbers left. 3 6 12 2 2 4 1 2

  10. Greatest Common Factor Multiply all of the prime numbers on the left side of the Ls to find the GCF. In the example, you would need to multiply 3 and 2. 3x2=6 The GCF for the pair of 6 and 12 is 6. 3 6 12 2 2 4 1 2

  11. Greatest Common Factor Let’s Try Another… 27 and 45

  12. Least Common Multiple Draw the L in your notebook like you did when you were working on the GCF. Place the set of numbers you are seeking to find the LCM for inside the L. Again, you need to leave a space in between the two numbers. 12 30

  13. Least Common Multiple Select a prime number that divides both numbers. For example, 12 and 30 are both divisible by 3. Put your 3 to the left of the L. 12 30 3

  14. Least Common Multiple Divide the set of numbers by the prime number you entered to the left of the L. The answer should be placed under the L. In the example, a 4 would go under the 12, and a 10 would go under the 30. 4 and 10 are not prime numbers, so another L is needed. Repeat the steps until you only have prime numbers remaining. This example would have another 2 to the left of the L with a 2 and a 5 under the L. 12 30 3 4 10 2 2 5

  15. Least Common Multiple Multiply all the numbers to the left of the L AND all of the prime numbers underneath of the last L together. The answer is your LCM. 3x2x2x5=60 The LCM for the numbers 12 and 30 is 60. 3 12 30 4 10 2 2 5

  16. Least Common Multiple Let’s Try Another… 16 and 20

  17. Find the GCF and LCM of the following: • GCF = 3, LCM = 30 • GCF = 10, LCM = 60 • GCF = 14, LCM = 42 • GCF = 6, LCM = 1080 • 6 and 15 • 20 and 30 • 14 and 42 • 24, 30 and 54

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