The Ladder Method: Factoring Numbers, Finding LCM & GCF
A method of factoring to find the Least Common Multiple (LCM) and Greatest Common Factor (GCF) of two numbers, simplifying fractions, demonstrated using the ladder method. Understand the process through visual examples and explanations by Becky Afghani.
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The Ladder Method
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 6 2 8 3 4 What number goes into both 6 and 8? 6 and 8 by the 2 go into both 3 and 4? No? Then you are done. Now divide both Does any # besides 1 Becky Afghani, LBUSD Math Curriculum Office, 2003
Lets 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. 6 2 8 The LCM of 6 and 8 is 24. x 3 4 =24 x 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. 6 2 8 The GCF of 6 and 8 is 2. 3 4 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. 6 8 6 2 6 8 8 simplifies to 3 3 4 4 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
Lets try some bigger numbers. Divide out all the common factors down the left side. 24 60 2 12 30 2 6 15 3 2 What number goes into both 24 and 60? besides 1 go into both 12 and 30? 6 and 15? Anything else? No? You re done. Does any # How about 5 Becky Afghani, LBUSD Math Curriculum Office, 2003
Find the LCM. 2 24 60 12 30 6 15 2 The LCM of 24 and 60 is 120. x 2 x 3 5 = 120 x x Becky Afghani, LBUSD Math Curriculum Office, 2003
Find the GCF. 2 24 60 12 30 6 15 3 2 The GCF of 24 and 60 is 12. x 2 x = 12 5 Becky Afghani, LBUSD Math Curriculum Office, 2003
24 Simplify . 60 24 2 24 60 12 30 6 15 3 2 60 2 simplifies to 2 . 5 5 Becky Afghani, LBUSD Math Curriculum Office, 2003
Practice. Find the LCM and GCF for 28 and 42. Simplify . 28 42 LCM = 2 7 2 3 = 84 2 7 28 42 14 21 2 3 GCF = 2 7 = 14 2 Simplified fraction =3 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. 2 7 28 42 1421 23 Becky Afghani, LBUSD Math Curriculum Office, 2003
