1. Name ____________________________________ Date __________________
Mrs. Labuski / Mrs. Rooney Period __________ Lesson 5-5 LCM / LCD
VOCABULARY DEFINITION EXAMPLE
The multiples of 3 are:
The product of 3, 6, 9, 12, 15, 18, 21, 24, 27,
MULTIPLE any number and 30
a whole number.
The multiples of 3 are:
3, 6, 9, 12, 15, 18, 21, 24, 27,
30
The smallest
LEAST The multiples of 4 are:
COMMON number that is a 4, 8, 12, 16, 20, 24, 28, 32, 36,
MULTIPLE multiple of two 40
LCM or more The common multiples are:
numbers. 12, 24,
The least common multiple is
12
The least 2 1
LEAST 3 4
COMMON common
DENOMINATOR multiple of two The LCD would be:
12
LCD or more
denominators.

2. There are two ways to find the Least Common Multiple.
The first is the List Method:
1. Find the LCM of 6 and 4
The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40
The LCM is _12__________
2. Find the LCM of 3, 6, and 9
The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
The multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72, 81, 90
The LCM is _18__________

3. The second method is to use Prime Factorization.
8=2 2 2
Write the prime factorization of each number.
12 = 2 2 3
8=2 2 2
Line up the common factors.
12 = 2 2 3
8=2 2 2
To find the LCM, multiply one number from each 12 = 2 2 3
column.    
2 2 2 3 = 24
3. Find the LCM of 6 and 8
The prime factorization of 6 is 2 3
The prime factorization of 8 is 2 2 2
The common factors are 2 2 2 3
The LCM is 24
4. Find the LCM of 2, 5, and 10
The prime factorization of 2 is 2
The prime factorization of 5 is 5
The prime factorization of 10 is 2 5
The LCM is 10

4. 5. Mr. Stevenson is ordering shirts and hats for his Boy Scout troop. There are 45
scouts in the troop. Hats come in packs of 3, and shirts come in packs of 5. What is
the least number of packs of each he should order to so that each scout will have 1
hat and 1 shirt, and none will be left over?
15 packs of hats and 9 packs of shirts
6. Tony wants to make 36 party bags. Glitter pens come in packs of 6. Stickers
come in sheets of 4, and balls come in packs of 3. What is the least number of each
package he should buy to have 1 of each item in every party bag, and no supplies
left over?
6 packs of pens, 9 sheets of stickers, and 12 packs of balls
7. Why do we need to find the Least Common Denominator?__________________
___________________________________________________________________
___________________________________________________________________
Find the LCD of the follow fractions:
8. 4 and 2 9. 5 and 7 10. 2 and 3
6 4 8 12 3 5
LCD _12_____ LCD __24___ LCD __15_____

5. Name ____________________________________ Date __________________
Mrs. Labuski / Mrs. Rooney Period __________ Lesson 5-5 LCM / LCD
VOCABULARY DEFINITION EXAMPLE
The multiples of 3 are:
MULTIPLE
The multiples of 3 are:
The multiples of 4 are:
LEAST
COMMON
MULTIPLE The common multiples are:
LCM
The least common multiple is
2 1
LEAST 3 4
COMMON
DENOMINATOR The LCD would be:
LCD

6. There are two ways to find the Least Common Multiple.
The first is the List Method:
1. Find the LCM of 6 and 4
The multiples of 6 are ___________________
The multiples of 4 are ___________________
The LCM is ___________
2. Find the LCM of 3, 6, and 9
The multiples of 3 are ___________________
The multiples of 6 are ___________________
The multiples of 9 are ___________________
The LCM is ___________

7. The second method is to use Prime Factorization.
8=2 2 2
Write the prime factorization of each number.
12 = 2 2 3
8=2 2 2
Line up the common factors.
12 = 2 2 3
8=2 2 2
To find the LCM, multiply one number from each 12 = 2 2 3
column. ↓ ↓ ↓ ↓
2 2 2 3 = 24
3. Find the LCM of 6 and 8
The prime factorization of 6 is ___________________
The prime factorization of 8 is ___________________
The common factors are ________________________
The LCM is ___________
4. Find the LCM of 2, 5, and 10
The prime factorization of 2 is ___________________
The prime factorization of 5 is ___________________
The prime factorization of 10 is ___________________
The LCM is ___________
5. Mr. Stevenson is ordering shirts and hats for his Boy Scout troop. There are 45
scouts in the troop. Hats come in packs of 3, and shirts come in packs of 5. What is

8. the least number of packs of each he should order to so that each scout will have 1
hat and 1 shirt, and none will be left over?
6. Tony wants to make 36 party bags. Glitter pens come in packs of 6. Stickers
come in sheets of 4, and balls come in packs of 3. What is the least number of each
package he should buy to have 1 of each item in every party bag, and no supplies
left over?
7. Why do we need to find the Least Common Denominator?__________________
___________________________________________________________________
___________________________________________________________________
Find the LCD of the follow fractions:
8. 4 and 2 9. 5 and 7 10. 2 and 3
6 4 8 12 3 5
LCD ______ LCD _______ LCD __________