Greatest Common Factor and Least Common Multiples GCF and LCM

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Greatest Common Factor and Least Common
MultiplesGCF and LCM
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What is the difference between a factor and a
multiple?FACTORS are numbers that divide evenly
into other numbers. Factors of 6 are (1, 2, 3,
6). Multiples are obtained by multiplying. Some
multiples of 6 are 6, 12, 18, 24
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Give me an example of a factor of 15
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Give me an example of a MULTIPLE of 15
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How would you find the GCF of 60 and 96?
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There are actually 2 ways. You can use prime
factorization, or write out all the prime
factors for each number.
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List the factors of 60
1,2,3,4,5,6,10,12,15,20,30,60
List the factors of 96
1,2,3,4,6,8,12,16,24,32,48,96 find the common
factors
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List the factors of 601,2,3,4,5,6,10,12,15,20,3
0,60List the factors of 961,2,3,4,6,8,12,16,24
,32,48,96find the largest factor 12
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or do prime factorization. Circle all the
primes the 2 numbers have in common and multiply
one set of them to get your GCF.
96
60
48
2
2
30
24
2
15
2
12
2
3
5
6
2
2 x 2 x 3 12
2
3
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Find the GCF (HCF) of 36, 24, 144 and 96
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96
24
36
144
12
96
24
36
48
2
2
12
18
2
24
2
6
9
2
2
12
2
3
2
3
3
6
2
144
2
3
12
12
3
4
2 x 2 x 3 12
3
4
2
2
2
2
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There are 2 ways to find the LCM as well. You
can list the multiples of the numbers or do prime
factorization. Find the LCM of 12 and 18
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Multiples of 12 areMultiples of 18
areThe smallest multiple the 2 numbers have
in common is the least common multiple.
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Multiples of 12 are12,24,36,48,60,72,.Multip
les of 18 are18,36,54,72,90,108,The
smallest multiple the 2 numbers have in common is
the least common multiple.
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or do prime factorization. Write down the
number they have in common only once, then write
down the leftover numbers. Multiply them all
together.
12
18
9
4
2
3
3
3
2
2
Numbers in common are 2 and 3 Leftover numbers
are 2 and 3 2 x 3 x 2 x 3 36
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Find the LCM of 35, 420 and 245
18
245
35
420
42
5
49
10
5
7
5
7
7
2
6
7
2
3
Numbers they have in common 5 and 7 Leftover
numbers 2, 3, 2, 7 Multiply them all together
5 x 7 x 2 x 3 x 2 x 7 2940