1. LEAST COMMON MULTIPLE
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2. Revision Find the prime factorization of each number:
36 = 2 x 2 x 3 x 3
76 = 2 x 2 x 19
105 = 3 x 5 x 7
145 = 5 x 29
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3. MULTIPLE
A Multiple of a number is the product of the number and any whole number.
For example, the multiples of 8 and 4 are listed below:
0 x 8 = x 4 = 0
1 x 8 = x 4 = 4
2 x 8 = x 4 = 8
3 x 8 = x 4 = 12
Multiples of 8
Multiples of 4
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4. COMMON MULTIPLE & LEAST COMMON MULTIPLE (LCM)
In the multiples of 8 and 4 - 0, 8, 16 and 24 are multiples of both 4 and 8. These numbers are common multiples of 4 and 8. The smallest number other than 0 is the Least Common Multiple.
Multiples of 4: 0, 4, 8, 12, 16, 20, 24, ……….
Multiples of 8: 0, 8, 16, 24, 32, 40, 48,……….
The least of the common multiples of 4 and 8, other than 0 is 8
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5. To find the LCM of two or more numbers, you can make a list
Method - 1
To find the LCM of two or more numbers, you can make a list
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6. Find the LCM by Making a List
Example - 1
Find the LCM by Making a List
Find the LCM of 6 and 12 by making a list.
Step 1 List the non-zero multiples.
multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120
Step 2 Identify the LCM from the common multiples.
The LCM of 6 and 12 is 12
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7. Try to do it now!!! Find the LCM of 4 and 16 by making a list:
Multiples of 4: 4, 8, 12, 16, 20, 24, 32, 26, 40, 44, 48, 52….
Multiples of 16: 16, 32, 48, 64, 80, ……
Common multiples are: 16, 32, 48,…..
Least Common Multiple is 16
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8. Prime Factors can also be used to find the LCM.
Method - 2
Prime Factors can also be used to find the LCM.
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9. Example - 2
Find the LCM of 15 and 25 by using prime factors:
Step 1 Write the prime factorization of each number.
3 x x 5
Step 2 Identify all common prime factors
15 = 3 x 5
25 = 5 x 5
Step 3 Find the product of the prime factors using each common prime factor once and any remaining factors. The LCM is 3 x 5 x 5 =75
Take only one 5
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10. your turn Find the LCM of each set of numbers: 4 and 7 4 7 2 X 2 7 X 1
Since there are no common factors, multiply all factors
i.e LCM = 2 x 2 x 7 x 1 = 28
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11. Have A Break
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12. Practice Problems
Find the LCM of each set of numbers by making a list.
2 and LCM = 10
2. 8 and LCM = 72
3. 4 and LCM = 20
4. 5 and LCM = 65
5. 3, 5 and LCM = 105
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13. More Practice Problems
Find the LCM by using prime factors:
16 and 20 LCM = 80
27 and 18 LCM = 54
15 and 18 LCM = 90
8 and 28 LCM = 56
12, 18 and 24 LCM = 72
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14. Use LCM to Solve a Problem
In a class, chairs are placed in rows so that either 6 or 10 members are in each row. What is the least number of students that can be seated in the class
Least number of students that can be seated in the class = LCM of 6 and 10
Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
Multiples of 10 = 10, 20, 30, 40, 50, 60, …..
Common multiples are: 30, 60, …
LCM = 30
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15. Solve this!
Columbus is planting his new garden. He knows he can plant all his roses by planting 12 or 15 rose bushes in every row. What is the least number of rose bushes he could have?
Multiple of 12: 12, 24, 36, 48, 60, 72,….
Multiples of 15: 15, 30, 45, 60, 75,….
LCM of 12 and 15 = 60
i.e he will be able to plant 60 rose bushes
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16. REVIEW
The smallest number other than 0 that is a multiple of two or more whole numbers is the LEAST COMMON MULTIPLE.
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17. WE WILL MEET YOU SOON WITH A NEW TOPIC
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