Least Common Multiples(LCM)

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Least Common Multiple(LCM)

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

Least Common Multiple

Ladder

Method

Find the LCM of 6 and 10STEP 1: Find the smallest prime number that

goes into all of the given numbers. Continue until you have at least one prime number.

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

2 ∙ 3 ∙ 5 = 30

6 102

3 5

LCM = 30

EXAMPLE

Find the LCM of 6 and 12

6 122

3 6

21

3

2 ∙ 3 ∙ 1 ∙ 2 = 12

LCM = 12

EXAMPLE

Find the LCM of 3 and 7

3 7

*Since both of the numbers are prime, simply multiply them together.

LCM = 21

3 ∙ 7 = 21

EXAMPLE

Find the LCM of 3, 9, and 12

9 12

3

3

4

3 ∙ 3 ∙ 4 = 36

LCM = 36 YOUR TURN

Find the LCM of 3, 7, and 10

7 10

7 ∙ 10 = 70

LCM = 70

YOUR TURN

Find the LCM of 2 and 8

2 82

1 4

2 ∙ 1 ∙ 4 = 8

LCM = 8YOUR TURN

Least Common Multiple(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

EXAMPLE

Find the LCM of 3, 5, and 6

3, 6, 30,12, 21,15,18, 24,9, 27,

6,

5,

12,

10, 20, 30,15, 25,

24,18, 30,

LCM = 30

EXAMPLE

Find the LCM of 3 and 5

3, 6, 9, 15

5,

12,

15 10,

YOUR TURN

Find the LCM of 6, and 9

1812,6,

189,

YOUR TURN

Hot dogs come in packs of 8. Hot dog buns come in packs of 12. What is the least number of packs of each Shawn

should buy to have enough to serve 24 people and have none left over?

3 packs of hot dogs and 2 packs of buns.

Debbie wants to invite 60 people to her party. Invitations come in packs of 12

and stamps come in sheets of 10. What is the least number of each she should buy to mail an invitation to each person

and have no supplies left over?

5 packs of invitations and 6 sheets of stamps

ITEM Number per

Pack

Invitations 12Balloons 30Paper plates 10Paper napkins 24Plastic cups 15Noise makers 5

You want to have an equal number of plastic cups and paper plates. What is the least number of packs of each you can buy?

3 packs of plates and 2 packs of cups

ITEM Number per

Pack

Invitations 12Balloons 30Paper plates 10Paper napkins 24Plastic cups 15Noise makers 5

You want to have an equal number of noisemakers and balloons at your party. What is the least number of packs of each you can buy?

1 pack of balloons and 6 packs of noise makers.

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