Apr 7 LCM and GCF.notebook
April 7, 2015
April 07, 2015
B Day
Learning Objective: I can find the LCM and the GCF
Review HW
GCF - Greatest Common Factor
HW: Finish worksheet
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Apr 7 LCM and GCF.notebook
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simplified fractions
have to be correct!
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Relatively Prime #'s - numbers
that have no factors in common
except 1.
Prime Numbers - numbers whose
only factors are l and itself!
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Let's recall how to find factor pairs of a number ...
24
1
2
3
4
What are they?
24
12
8
6
Try this one ...
1)
Start with 1 on the left and
write it's pair on the right.
2)
but the
are
Continue
withsteps
each integer
until
you get
a pair of integers
fairly
easy!
that are close to each other.
3)
Check any whole numbers in
between these two factors.
36
1
2
3
4
6
36
18
12
9
6
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Apr 7 LCM and GCF.notebook
April 07, 2015
REMEMBER THESE DIVISIBILITY RULES??
You need
them!
613
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Apr 7 LCM and GCF.notebook
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are not widely used but are presented so you can see them.
If you double the last digit and subtract it from the rest of
the number and the answer is 0 or divisible by 7 (you may
need to repeat this process again to determine if the
answer is 0 or the rest of the number is too big to know).
672
2 2=4
67 4 = 63 and 63 is divisible by 7 so 672 is divisible by 7
1525
5
2 = 10
152 10 = 142 not sure?? Then do it again with 142.
2 2=4
14 4 = 10 and 10 is not divisible by 7
so 1525 is not divisible by 7
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Apr 7 LCM and GCF.notebook
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Now let's recall how we find the greatest common
factor (GCF)
We circled all the common
factors in both lists and the
largest one was the GCF.
24
1
2
3
4
24
12
8
6
36
1
2
3
4
6
36
18
12
9
6
GCF (24, 36) = 12
This method assumes you
find ALL the factor pairs!
What if the pair of numbers
were 275 and 1070?
Is there an easier way??
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Apr 7 LCM and GCF.notebook
April 07, 2015
Now let's recall how we find the greatest common
factor (GCF)
We circled all the common
factors in both lists and the
largest one was the GCF.
24
1 24
2 12
3 8
4
6
36
1
2
3
4
6
36
18
12
9
6
GCF (24, 36) = 12
Oh, my. All this work
and what if we miss one?
Let's take another
look at our LCM
method ...
24
2
=
36
3
3
2
24
72
=
36
72
LCM (24, 36) = 72
and specifically look at the original fraction and the
simplified fraction
24
2
=
36
3
Notice that
24 ÷ 2 = 12
36 ÷ 3 = 12
and 12 is the GCF.
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Apr 7 LCM and GCF.notebook
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This is the method I want you to use.
Does it ALWAYS work?
YES!!
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Apr 7 LCM and GCF.notebook
LCM (16, 24)
April 07, 2015
16
24
write it as
a fraction
=
2
3
simplify
it
3
16
*
2
24
turn it
upside
down
=
multiply
with the
original
48
48
both
numbers
are the
LCM
LCM (16, 24) = 48
When we simplified
16 ÷ 2 = 8
24 ÷ 3 = 8
16 , we got 2 .
3
24
GCF (16, 24) = 8
The steps:
1) set the two numbers up as a fraction
2) simplify the fraction completely
3) using the original fraction and the
simplified fraction, divide the numerators
The answer is your GCF.
4) Do the same with your denominators. If the answer
is not the same as the numerators answer, then you
made a mistake in the simplifying. Find it and fix it.
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Apr 7 LCM and GCF.notebook
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LCM (125, 150)
Remember
this one from
yesterday?
125 = 5
6
150
write it as
a fraction
simplify
it
6
125
750
=
*
5
150
750
turn it
upside
down
multiply
with the
original
both
numbers
are the
LCM
LCM (125, 150) = 750
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), you will get a common factor but not the largest
common factor (GCF).
Find the GCF (125, 150)
125 = 5
6
150
125 ÷ 5 = 25
150 ÷ 6 = 25
GCF (125, 150) = 25
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Apr 7 LCM and GCF.notebook
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Let's try these ...
GCF (48, 60) = 12
48
4
=
60
5
48 ÷ 4 = 12
60 ÷ 5 = 12
GCF (13, 15) = 1
13
13
=
15
15
13 ÷ 13 = 1
15 ÷ 15 = 1
If the two #'s cannot be
simplified, the GCF is
ALWAYS 1.
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Apr 7 LCM and GCF.notebook
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1) Find the GCF ( 8, 40)
8 = 1
40
5
8÷1=8
40 ÷ 5 = 8
GCF ( 8, 40) = 8
2) Find the GCF ( 13, 15)
13 = 13
15
15
13 ÷ 13 = 1
15 ÷ 15 = 1
GCF ( 13, 15) = 1
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these 4 cannot
be simplified.
Apr 7 LCM and GCF.notebook
April 07, 2015
If the fraction
cannot be simplified
the GCF is always 1.
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