the ladder method

The Ladder Method

For Finding LCD, GCF and

Simplifying Fractions

Becky Afghani, LBUSD Math Curriculum Office, 2003

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• simplify a fraction with these

numbers as numerator and denominator

Becky Afghani, LBUSD Math Curriculum Office, 2003

Use the ladder to factor6 and 8

You will divide out any common factors of the two numbers

What number goesinto both 6 and 8?

Now divide both6 and 8 by the 2

Does any # besides 1go into both 3 and 4?No? Then you are done.

Becky Afghani, LBUSD Math Curriculum Office, 2003

Let’s find the Least Common Multiple (LCM) of

6 and 8The LCM is the product of all the

numbers on the left and the bottom.

The LCMof

6 and 8is 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 GCFof

6 and 8is 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.

86

simplifiesto

86

43

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 numbergoes into both

24 and 60?Does any #

besides 1go into both 12 and 30?How about6 and 15?

Anything else?No?

You’re done.

Becky Afghani, LBUSD Math Curriculum Office, 2003

x

x

xx

Find the LCM.

=120

The LCMof

24 and 60is 120.

Becky Afghani, LBUSD Math Curriculum Office, 2003

x

x

Find the GCF.

=12

The GCFof

24 and 60is 12.

Becky Afghani, LBUSD Math Curriculum Office, 2003

Simplify .6024

simplifies to

.

6024

52

Becky Afghani, LBUSD Math Curriculum Office, 2003

Practice. Find the LCM and Practice. Find the LCM and

GCF for 28 and 42. Simplify GCF for 28 and 42. Simplify

.. 4228

LCM = 2 7 2 3 = 84

GCF = 2 7 = 14 Simplified fraction =

32

Becky Afghani, LBUSD Math Curriculum Office, 2003

Extension QuestionsExtension 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.