finding gcf’s and lcm’s grade 6. do now (pre-test) study island responders 5 minutes
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Finding GCF’s and LCM’s
Grade 6
Do Now (Pre-Test)
Study Island Responders
5 minutes
Learning ObjectiveStudents will be able to identify factors and multiples of a positive integer, common factors, common multiples, the greatest common factor, and the least common multiple of a set of positive integers. 5N13 - Calculate multiples of a whole number and the least common multiple of two numbers 5N14 - Identify the factors of a given number 5N15 - Find the common factors and the greatest common factor of two numbers
Vocabulary
• GCF – the factor with the greatest value that is shared by all numbers.
• Multiples – the product of a number and a non zero number.
• LCM – the multiple with the least value that is shared by all numbers.
Finding the Greatest Common Factor
of Two Numbers
must be common to both numbers. WeWe are looking for a factor. The factor
need to pick the greatest of suchcommon factors.
Method 1
The GCF of 36 and 90
1) List the factors of each number.
36: 1 2 3 4 6
36 18 24 9
2) Circle the common factors.
90: 1 2 3 5 6 9
90 45 30 18 15 10
3) The greatest of these will be your Greatest Common Factor:
18
Method 2
The GCF of 36 and 90
1) Prime factor each number.
36 = 2 ● 2 ● 3 ● 3
2) Circle each pair of common prime factors.
90 = 2 ● 3 ● 3 ● 5
3) The product of these common prime factors will be
2 ● 3 ● 3 = 18the Greatest Common Factor:
Finding the Least Common Multiple
of Two Numbers
must be common to both numbers. WeWe are looking for a multiple. The multiple
need to pick the least of suchcommon multiples.
Method 1
The LCM of 12 and 15
1) List the first few multiples of each number.
12: 12 24 36 48 60 72 84 90 108 120
2) Circle the common multiples.
15: 15 30 45 60 75 90 105 120 135
3) The least of these will be your Least Common Multiple:
60
Method 2
The LCM of 12 and 15.
1) Prime factor each number.
12 = 2 ● 2 ● 3
2) Circle each pair of common prime factors.
15 = 5 ● 3
4) Multiply together one factor from each circle to get the
3 ● 2 ● 2 ● 5 = 60Least Common Multiple :
3) Circle each remaining prime factor.
Note that the common factor, 3, was only used once.
Method 3: Find both GCF and LCM at Once.
1) Make the following table.
72 90
The GCF and LCM of 72 and 90
2) Divide each number by a common factor.
3) Divide the new numbers by a common factor. Repeat this process until there is no longer a common factor.
9
8 1024 5
The product of the factors on the left is the GCF:
9 ● 2 = 18
The product of the factors on the left AND bottom is the LCM: 9 ● 2 ● 4 ● 5 = 360
Method 3: Find both GCF and LCM at Once.
1) Make the following table.
96 144
One more example: The GCF and LCM of 96 and 144
2) Divide each number by a common factor.3) Divide the new numbers by a common factor. 4) Repeat this process until there is no longer a common factor.
2
48 7268 12
The product of the factors on the left is the GCF:
2 ● 6 ● 4 = 48
The product of the factors on the left AND bottom is the LCM: 2 ● 6 ● 4 ● 2 ● 3 = 288
42 3
Note that you can pick any common factor to start and any remaining common factor for each step. Try starting by dividing by 3 to see that this is so.
Independent Practice
• Group 1
• Group 2
• Group 3
Quick Quiz
Study Island (Responders)
“Games”
Journal & Summary
• Nine people plan to share equally 24 stamps from one set and 36 stamps from another set. Explain why 9 people cannot share the stamps equally.
• What's is the LCM for two numbers that have no common factors greater than 1? Explain your reasoning.
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