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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 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 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.
