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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 • simplify a fraction with these numbers as numerator and denominator Becky Afghani, LBUSD Math Curriculum Office, 2003

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

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. Becky Afghani, LBUSD Math Curriculum Office, 2003

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

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. Becky Afghani, LBUSD Math Curriculum Office, 2003

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

How can we use the Ladder Method to simplify ? The simplified numerator and denominator are on the bottom. simplifies to Becky Afghani, LBUSD Math Curriculum Office, 2003

Which numbers in the ladder give you the simplified fraction? The numbers on the bottom of the ladder are your simplified numerator and denominator. Becky Afghani, LBUSD Math Curriculum Office, 2003

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

Find the LCM. The LCM of 24 and 60 is 120. x x = 120 Becky Afghani, LBUSD Math Curriculum Office, 2003

Find the GCF. The GCF of 24 and 60 is 12. x 12= x Becky Afghani, LBUSD Math Curriculum Office, 2003

Simplify . simplifies to. Becky Afghani, LBUSD Math Curriculum Office, 2003

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

Extension Questions 1. Do you have to factor out prime numbers? 2. Can you factor three numbers at once and still get the right GCF and LCM? Try factoring small numbers to find out - like 4, 6, and 8. Becky Afghani, LBUSD Math Curriculum Office, 2003