MJ2A

5.6 – Least Common Multiple

Bellwork

• Add or subtract. Write your answer in simplest form.

1. 1 + 1

10 3

2. 1 - 2

4 3

3. 6 1 - 4 1

2 5

Assignment Review

• Text p. 235 # 11 – 30

Before we begin…

• Please take out your notebook and get ready to work…

• Today we will look at the Least Common Multiple (LCM) of 2 or more numbers…

• For those students that do not know their multiplication tables…knowing this will help you when you have to convert fractions to a common denominator

• Raise your hand if you can tell the class what a least common multiple is…

Objective 5.6

• Students will find the least common multiple of two or more numbers.

Least Common Multiple

• A multiple of a number is the product of that number and a whole number.

Example:5 x 0 = 05 x 1 = 55 x 2 = 10 etc…

• We can say that the multiples of 5 are 0, 5, 10, 15, etc…

• As the name suggests the least common multiple of 2 or more numbers is the smallest multiple that the numbers have in common.

Finding the LCM

• There are a number of methods that can be used to find the LCM.

• You can:

1. List the multiples of each number

2. Do a factor tree

3. Use the cake method• For today’s lesson we will look at the cake

method as that is the easiest method…

Example

• Find the LCM of 4 and 6

2 4, 6

2 3• The LCM will be 2x2x3 = 12• Notice that the numbers form the shape

of an L to help you remember what to multiply

Example

• Find the LCM of 16 & 24

2 16, 24

2 8 12

2 4 6

2 3• The LCM is 2 x 2 x 2 x 2 x 3 = 48

How does this help with Common Denominators?

• Knowing the LCM can help you with finding a common denominator when adding or subtracting unlike fractions

• In the previous example suppose you were adding 8/16 & 3/24, you could use the cake method to find the LCM and therefore, know that the smallest number that both 16 and 24 go into is 48

• When using the LCM you minimize the need to simplify the fractions

Your Turn

• In the notes section of your notebook write and find the LCM of the following:

1. 6 & 8

2. 12 & 30

3. 10 & 14

LCM of Monomials

• You can also use the cake method to find the LCM of algebraic monomials

• Find the LCM of 12b2 & 8ab

2b 12b2, 8ab

2 6b 4a

3b 2a• The LCM = 2b x 2 x 3b x 2a = 24ab2

Your Turn

• In the notes section of your notebook write the monomials and then find the LCM of each

1. 12x2y2 & 6y3

2. 15b2 & 25b3

Summary

• In the notes section of your notebook summarize the key concepts covered in today’s lesson.

• Today we discussed• LCM – what is it?• Name 3 methods to find the LCM• How can knowing LCM help you with unlike

fractions?

Assignment

• Practice Skills workbook lesson 5.6

Reminder• This assignment is due tomorrow• I do not accept late assignments• Do the odd problems only• Write them on a separate sheet of paper

and show how you got your answer (no work = no credit)