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The Ladder Method

The Ladder Method. For Finding LCD, GCF and Simplifying Fractions. Becky Afghani, LBUSD Math Curriculum Office, 2003. The Ladder Method. is a method of factoring which allows you to factor two numbers at once in order to… find the LCM of the two numbers find the GCF of the two numbers.

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The Ladder Method

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  1. The Ladder Method For Finding LCD, GCF and Simplifying Fractions Becky Afghani, LBUSD Math Curriculum Office, 2003

  2. The Ladder Method... is a method of factoring which allows you to factor two numbers at once in order to… • find the LCM of the two numbers • find the GCF of the two numbers Becky Afghani, LBUSD Math Curriculum Office, 2003

  3. Use the ladder to factor6 and 8 You will divide out any common factors of the two numbers 2 6 8 3 4 What number goes into both 6 and 8? Now divide both 6 and 8 by the 2 Does any # besides 1 go into both 3 and 4? No? Then you are done. Becky Afghani, LBUSD Math Curriculum Office, 2003

  4. x x Let’s find the Least Common Multiple (LCM) of 6 and 8 The LCM is the product of all the numbers on the left and the bottom. The LCM of 6 and 8 is 24. 2 6 8 3 4 =24 Becky Afghani, LBUSD Math Curriculum Office, 2003

  5. The “L” shape gives you the LCM: multiply the numbers on the left and bottom. Which numbers in the ladder give you the LCM? # # # # # # # # # # # Becky Afghani, LBUSD Math Curriculum Office, 2003

  6. What about the Greatest Common Factor (GCF) of 6 and 8? The GCF is the product of all the numbers on the left. The GCF of 6 and 8 is 2. 2 6 8 3 4 Becky Afghani, LBUSD Math Curriculum Office, 2003

  7. Multiply the numbers on the left only for the GCF. Which numbers in the ladder give you the GCF? # # # # # # # # # # # Becky Afghani, LBUSD Math Curriculum Office, 2003

  8. Let’s try some bigger numbers. Divide out all the common factors down the left side. 2 24 60 What number goes into both 24 and 60? Does any # besides 1 go into both 12 and 30? 2 12 30 How about 6 and 15? Anything else? 3 6 15 No? You’re done. 2 5 Becky Afghani, LBUSD Math Curriculum Office, 2003

  9. 2 24 60 x 2 12 30 x 3 6 15 x x 2 5 Find the LCM. The LCM of 24 and 60 is 120. = 120 Becky Afghani, LBUSD Math Curriculum Office, 2003

  10. 2 24 60 x 2 12 30 x 3 6 15 2 5 Find the GCF. The GCF of 24 and 60 is 12. = 12 Becky Afghani, LBUSD Math Curriculum Office, 2003

  11. Practice. Find the LCM and GCF for 28 and 42. LCM = 2  7  2  3 = 84 2 28 42 GCF = 2  7 = 14 7 14 21 2 3 Becky Afghani, LBUSD Math Curriculum Office, 2003

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