Greatest Common Factor (GCF)and Least Common Multiples(LCM)

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Greatest Common Factor (GCF)and Least Common
Multiples(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, list 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.
60, 96
2
2 x 2 x 3 12
2
30, 48
15, 24
3
5, 8
10
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
7
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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Find the GCF and LCM of12 and 13
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Find the GCF and LCM of 27, 21, 33 and 15
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GCF and LCM Problem Solving

• How can you tell if a word problem requires you
  to use Greatest Common Factor or Least Common
  Multiple to solve?

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GCF Example Applying what we have learned

• Samantha has two pieces of cloth. One piece is 72
  inches wide and the other piece is 90 inches
  wide. She wants to cut both pieces into strips of
  equal width that are as wide as possible. How
  wide should she cut the strips?

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LCM Example Applying what we have learned

• Ben exercises every 12 days and Isabel every 8
  days. Ben and Isabel both exercised today. How
  many days will it be until they exercise together
  again?

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Question 1

• Mrs. Evans has 120 crayons and 30 pieces of paper
  to give to her students. What is the largest of
  students she can have in her class so that each
  student gets equal of crayons and equal of
  paper.

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Question 2

• Rosa is making a game board that is 16 inches by
  24 inches. She wants to use square tiles. What
  is the larges tile she can use?

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Question 3

• Z100 gave away a Z 100 bill for every 100th
  caller. Every 30th caller received free concert
  tickets. How many callers must get through before
  one of them receives both a coupon and a concert
  ticket?

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Question 4

• Two bikers are riding a circular path. The first
  rider completes a round in 12 minutes. The second
  rider completes a round in 18 minutes. If they
  both started at the same place and time and go in
  the same direction, after how many minutes will
  they meet again at the starting point?

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Question 5

• Sean has 8-inch pieces of toy train track and
  Ruth has 18-inch pieces of train track. How many
  of each piece would each child need to build
  tracks that are equal in length?

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Question 6

• I am planting 50 apple trees and 30 peach trees.
  I want the same number and type of trees per row.
  What is the maximum number of trees I can plant
  per row?