1. Least Common Multiples And Greatest Common Factor

2. Least Common Multiples
Lesson
3.4.5
Least Common Multiples
California Standards:
Number Sense 2.1
Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation.
Number Sense 2.4
Determine the least common multiple and the greatest common divisor of whole numbers; use them to solve problems with fractions (e.g., to find a common denominator to add two fractions or to find the reduced form for a fraction).
What it means for you:
You’ll learn how to find the lowest number that two numbers both divide into exactly. You’ll also see how this can help you with adding and subtracting fractions.
Key words:
least common multiple
greatest common factor

3. Lesson
3.4.5
Least Common Multiples
Today we are going to learn about Lowest Common Multiples and Greatest Common Factor. First let’s examine the parts of a multiplication equation.
The Least Common ulte Is Less Than the Others
MULTIPLE

4. Example: What is the LCM of 10 and 30?
Lesson
3.4.5
Least Common Multiples
Definition
Least Common Multiple (LCM): The lowest multiple of two or more numbers.
Example: What is the LCM of 10 and 30?
10 x 1 = 10
10 x 2 = 20
10 x 3 = 30
10 x 4 = 40
10 x 5 = 50
10 x 6 = 60
30 x 1 = 30
30 x 2 = 60
30 x 3 = 90
So the least common multiple of 10 and 30 is 30.

5. When do you use LCM? Least Common Multiples 3.4.5
Lesson
3.4.5
Least Common Multiples
When do you use LCM?
The Least Common ulte Is Less Than the Others 30 2 10 1 +
When you need to add fractions with different denominators!

6. Example: What is the GCF of 20 and 30?
Lesson
3.4.5
Least Common Multiples
Definition
Greatest Common Factor (GCF): The largest factor shared by two or more numbers.
1 x 30
2 x 15
3 x 10
5 x 6
Example: What is the GCF of 20 and 30?
1 x 20
2 x 10
4 x 5
The factors of 20 are 1, 2, 4, 5, 10, and 20
The factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30

7. When do you use GCF? Least Common Multiples 3.4.5
Lesson
3.4.5
Least Common Multiples
When do you use GCF?
The Least Common ulte Is Less Than the Others 30 20
When you need to SIMPLIFY fractions!

8. with a factor tree. Let’s try some!
Lesson
3.4.5
Least Common Multiples
You can find the Lowest Common Multiple (LCM) and the Greatest Common Factor (GCF)
with a factor tree. Let’s try some!
The LeastThan the Others

9. Least Common Multiples
Lesson
3.4.5
Least Common Multiples
Example 1
Find the LCM and GCF of 20 and 12.
Solution
So the least common multiple of 20 and 12 is 60 .
Solution follows…

10. Least Common Multiples
Lesson
3.4.5
Least Common Multiples
Example 2
Find the LCM and GCF of 16 and 28.
Solution
So the least common multiple of 16 and 28 is 112.
Solution follows…

11. Least Common Multiples
Lesson
3.4.5
Least Common Multiples
Example 3
Find the LCM and GCF of 12 and 44. .
Solution
So the least common multiple of 12 and 44 is: 12 × 44 ÷ 4 = 132
Solution follows…

12. Least Common Multiples
Lesson
3.4.5
Least Common Multiples
Guided Practice
Find the least common multiple and greatest common factor.
1. 4, , 50
3. 12, , 25
Solution follows…

13. Least Common Multiples
Lesson
3.4.5
Least Common Multiples
Independent Practice
Find the LCM and GCF.
7. 30, , 12
9. 14, , 30
Solution follows…

14. LCM and GCF: Fractions with Different Denominators

15. LCM and GCF 3.4.5 What is + ? Solution: = + 5 1 3 15 5 + 3 8 3 1 5 1
Lesson
3.4.5
LCM and GCF
Example 1 3 1 5 1
What is ?
Solution: = + 5 1 3 15
5 + 3 8

16. Lesson
3.4.5
LCM and GCF
Example 2 40 3 16 5
What is ?

17. Lesson
3.4.5
LCM and GCF
Example 3
What is 2 ½ + 3 ¼ =

18. Least Common Multiples
Lesson
3.4.5
Least Common Multiples
Guided Practice
Use factor trees to find the GCF and LCM. Solve the equations once they have the same denominator. 10 13 15 9 + 4 9 + 5 6 39 30 18 57 19 10 + = 8 18 15 23 + =
1. 2.
3. 4. 10 5 1 6 + 5 6 – 1 8 5 30 15 20 2 3 + = 20 24 3 17 = –
Solution follows…

19. Least Common Multiples
Lesson
3.4.5
Least Common Multiples
Guided Practice
Solve the following problems. 20 2 + 15 3 42 13 14 5 + 12 60 6 18 3 10 + = 13 42 15 28 2 3 + = 5. 6.
**TICKET PROBLEM 4 6 – 2 8 16 24 6 10 5 12 – =
Solution follows…

20. Least Common Multiples
Lesson
3.4.5
Least Common Multiples
Independent Practice
Find the LCM and GCF for problems 7-15 by making factor trees. Then add or subtract the fractions. 2 3 – 1 4 3 4 – 1 2 1 9 + 2 7 5 12 1 4 25 63 + 10 2 25 15 8 9 – 5 6 12 13 3 4 4 5 1 18 1 3 – + 11 8 44 18 18 12 + 15 13 25 22 23 15 14 9 – 10 9 35
Solution follows…

21. Least Common Multiples
Lesson
3.4.5
Least Common Multiples
Independent Practice
Work out the sums and differences in Exercises 26– Give your answers in their simplest form. + 75 7 35 15 45 1 – 27 4 + 24 1 56 15
274
525 17
135 13 42 49 10 21 6 + 30 1 7 9 + 56 10 – 42 31 24 49 73 90 47 84
Solution follows…

22. Least Common Multiples
Lesson
3.4.5
Least Common Multiples
Round Up
Pausing for a second to find the least common multiple before trying to add or subtract two fractions with different denominators is a good way to avoid having to deal with really big numbers.
Smaller numbers also make simplifying at the end easier.