Apr 6 LCM and GCF.notebook
April 6, 2015
April 06, 2015
A Day
Learning Objective: I can find the LCM and the GCF
LCM - Least Common Multiple
HW: Finish worksheet
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Apr 6 LCM and GCF.notebook
April 06, 2015
Definitions:
Multiple: All the numbers you get if you skip count using that
number.
means to multiply
More mathematically ...
A multiple of a number is the product of that
number and any other non-negative whole number.
As an example
for 3: 3, 6, 9, 12, 15, 18, 21, etc. are multiples.
Notice ...
3 x 1 = 3, 3 x 2 = 6, 3 x 3 = 9, 3 x 4 = 12, 3 x 5 = 15 , etc.
Common Multiple: A multiple shared by two or more numbers.
Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, etc.
The common multiples are 12, 24, 36, etc.
The common multiples are multiples of the first (smallest)
common multiple.
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Apr 6 LCM and GCF.notebook
April 06, 2015
Definition
Least Common Multiple - The very first (smallest)
common multiple between two or more numbers.
We usually abbreviate the least common multiple with
the letters LCM .
When we want to find the LCM of two numbers, such
as 3 and 4, we write it the following way ...
LCM (3,4) = 12
where 12 is the LCM
Please begin to write it this way!
When we are wanting to find the least common denominator, it
is actually the LCM we are wanting to find.
such as ...
LCM (3,4,5,6) = 60
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Apr 6 LCM and GCF.notebook
April 06, 2015
Find the LCM (5, 8).
5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, ...
8: 8, 16, 24, 32, 40, 48, 54, ...
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the LCM (5, 8) = 40
You may have noticed that the LCM (3,4) = 12
2
and the LCM (5,8) = 40
Can we always just
multiply the two numbers?
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Apr 6 LCM and GCF.notebook
April 06, 2015
Is there an easier way than listing all the multiples of
each and hoping we don't make a mistake?
Why yes there is ...
Consider ... 1
6: 6, 12, 18, 24, ...
9: 9, 18, ...
Now, look at the fraction
6
92
and3 simplify it ...
turn the simplified fraction
3 18
6
upside down and multiply it
9 * 2 = 18
with
the original one ...
4
notice both numbers
are the LCM!
6 = 2
9
3
5
5
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Apr 6 LCM and GCF.notebook
April 06, 2015
LCM (16, 24)
16
24
=
write1it as
a fraction
2
3
2
simplify
it
3
16
2 * 24
3 it
turn
upside
down
4
multiply
with the
original
=
48
48
5
both
numbers
are the
LCM
LCM (16, 24) = 48
Let's check:
16, 32, 48, 64
24, 48, 72
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Apr 6 LCM and GCF.notebook
Try another ...
125 = 5
6
150
write1it as
a fraction
2
simplify
it
April 06, 2015
LCM (125, 150)
6
750
125
=
5 * 150
750
3 it
turn
upside
down
4
multiply
with the
original
5
both
numbers
are the
LCM
LCM (125, 150) = 750
Make sure you write your answer in this format!
WARNING ....
The most common error is not simplifying the
fraction all the way. If you don't, you will get a
common multiple, but not the first common
multiple (the LCM).
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Apr 6 LCM and GCF.notebook
April 06, 2015
Let's practice ....
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Apr 6 LCM and GCF.notebook
April 06, 2015
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Apr 6 LCM and GCF.notebook
April 06, 2015
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