Transcript The Ladder Method

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
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
goes
Nownumber
divide both
Does
any6#and
besides
1
into
both
8?
6 and
8both
by
the
2 done.
No?
Then
you
go
into
3are
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
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
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
Practice. Find the LCM and GCF
for 28 and 42.
LCM = 2  7  2  3 = 84
GCF = 2  7 = 14
Becky Afghani, LBUSD Math Curriculum Office, 2003