Least Common Multiples (LCM)

Course 1

5-1 Least Common Multiple

Least Common Multiples(LCM)

Course 1

5-1 Least Common Multiple

Smallest number that is a multiple of 2 or more numbers.

Definition

• LCM of 3 and 5

LCM: Ladder Method

STEP 2: Multiply all of the numbers on the side and on the bottom row.

2 ∙ 3 ∙ 5 = 30 LCM = 30

STEP 1: Find the smallest prime number that goes into all of the given numbers. Continue until you have at least one prime number.

Find the LCM of 6 and 10

6 102

3 5

Find the LCM of 6 and 12

6 122

3 6

21

3

2 ∙ 3 ∙ 1 ∙ 2 = 12

LCM = 12

No Common Factors - Primes

15 4

If the numbers have no common factors, simply multiply them together.

LCM = 60

15 ∙ 4 = 60

3 7

LCM = 213 ∙ 7 = 21

Find the LCM of 9 and 12

9 12

3

3

4

3 ∙ 3 ∙ 4 = 36

LCM = 36 YOUR TURN

Find the LCM of 7 and 10

7 10

7 ∙ 10 = 70

LCM = 70

YOUR TURN

Find the LCM of 20 and 30

20 302

10 15

32

5

2 ∙ 5 ∙ 2 ∙ 3 = 60

LCM = 60 YOUR TURN

LCM: Listing Method

Find the LCM of 8 and 12

Step 1: List the multiples of each number

Step 2: Circle the smallest number that is in all the lists.

Step 3: Write the answer

8, 16, 24, 32

12, 24

LCM = 24

Find the LCM of 6, and 9

1812,6,

189,

YOUR TURN

Course 1

5-1 Least Common Multiple

Using Multiples to Find the LCM

Find the least common multiple (LCM).

Method 2: Use a list.

4: 4, 8, 12 , 16, 20, 24, 28, 32, 36, 40, 44, . . .

5: 5, 10, 15, 20, 25, 30, 35, 40, 45, . . .

8: 8, 16, 24, 32, 40, 48, . . .

LCM: 40

List multiples of 4, 5, and 8.

Find the smallest number that is in all the lists.

4, 5, and 8

Word Problems

Course 1

5-1 Least Common Multiple

Problem Solve: Consumer Application

English muffins come in packs of 8, and eggs come in cartons of 12. If there are 24 students, what is the least number of packs and cartons needed so that each student has a muffin sandwich with one egg and there are no muffins left over?

There are 24 English muffins and 24 eggs.

So 3 packs of English muffins and 2 cartons of eggs are needed.

Course 1

5-1 Least Common Multiple

8 122

4 6

32

2

John has a baseball game every 6 days and a football game every 9 days. John is

playing both a baseball and a football game today. How many days is it until

John plays both a baseball and a football game on the same day again?

18 days

Fatima is buying hot dogs for a class picnic. Hot dogs are sold in packages of 10. Hot

dogs buns are sold in packages of 8. What is the smallest number of hot dogs and buns Fatima can buy to have an equal number of

each?

40 hot dogs & buns, 4 packs of hot dogs, and 5 packs of buns