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?
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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 3 ways. You can use prime
factorization, write out all the prime factors
for each number or extract common prime numbers.
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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
9
or you can extract the common prime factors of
60 and 96 and form a product to give the GCF.
This, to me, is the easiest way. Try it!
60, 96
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2 x 2 x 3 12
2
30, 48
15, 24
3
5, 8
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Find the GCF (HCF) of 36, 24, 144 and 96
11
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
12
36, 24, 144, 96
2
2 x 2 x 3 12
18, 12, 72, 48
2
9, 6, 36, 24
3
3
2
12
8
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There are 3 ways to find the LCM as well. You
can list the multiples of the numbers, do prime
factorization, or extract the prime factors from
either one or both numbers.Find the LCM of 12
and 18
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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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Rememberthe numbers you pull out have to be
prime numbers!
12, 18
2
6, 9
2
3
3, 9
1, 3
3
1
1
2 x 2 x 3 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
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primes
35, 420, 245
5
7, 84, 49
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1, 12, 7
7
3
1, 12, 1
1, 4, 1
2
1, 2, 1
2
1, 1, 1
5 x 7 x 7 x 3 x 2 x 2 2940
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Find the GCF and LCM of 28 and 63
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7 28 63 4 9
GCF 7
LCM 7 x 4 x 9 252
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Find the GCF and LCM of12 and 13
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1 12 13
GCF 1
LCM 1 x 12 x 13 156
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Find the GCF and LCM of 27, 21, 33 and 15
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3 27 21 33 15 9 7 11 5
GCF 3
LCM 3 x 9 x 7 x 11 x 5 10,395
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Start tonights homework. No calculators!