Least Common Multiple

Objective: To find the least common multiple

Vocabulary:

Least Common Multiple (LCM):

The least non-zero common multiple of two or more numbers.

Method 1: Make a list of multiples

Ex: Find the LCM of 4 and 9

4:9:

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 449, 18, 27, 36, 45,

36 is the LCM of 4 and 9

Method 2: Prime factorization with factor trees.

Find the LCM of 10 and 12

10 12

5 2

4

32 2

10 = 2 • 512 = 2•2•3

2•2•3•5 = 60

Multiply the factors, using the common factors only once

Method 3: prime factorization using upside-down division

Find the LCM of 12 and 16

12 162623

12 =

16 =2•2 • 3

282422

2•2•2•2

2•2•2•2•3= 48

Multiply the factors using the common factors only once.

Find the LCM of 24 and 84

24 84212 4226 7 No more common factors

2•2•6•7 = 168

Find the LCM of the following

1) 8 and 22

2) 18 and 20

3) 40 and 24

4) 25 and 45

88

180

120

225

 

 

 

 

You are having a barbeque and will be serving hot dogs. You notice that hot dogs are sold in packs of 6 and hot dog buns are sold in packs of 8. You want to have the same number of hot dogs as buns without any left over. How many packs of each should you buy?

Hot Dogs: 6: 6, 12, 18, 24, 30, 36

HD Buns: 8: 8, 16, 24, 32,40

4 packs of Hot Dogs

3 packs of Buns