Transcript Least Common Multiples (LCM)

Least Common Multiples
(LCM)
M6N1c
Least Common Multiple
(LCM)
• Smallest number that is a multiple of 2 or
more numbers
Least Common Multiple
Ladder
Method
EXAMPLE
Find the LCM of 6 and 10
STEP 1: Find the smallest prime number that
goes into all of the given numbers. Continue
until you have at least one prime number.
2
6 10
3
5
STEP 2: Multiply all of the numbers on the
side and on the bottom row.
2 ∙ 3 ∙ 5 = 30
LCM = 30
EXAMPLE
Find the LCM of 6 and 12
2
6
3
12
3
6
1
2
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.
3 ∙ 7 = 21
LCM = 21
Find the LCM of 3, 9, and 12
3 9 12
3
4
3 ∙ 3 ∙ 4 = 36
LCM = 36
Find the LCM of 3, 7, and 10
7
7 ∙ 10 = 70
LCM = 70
10
Find the LCM of 2 and 8
2
2 8
1 4
2∙1∙4=8
LCM = 8
Least Common Multiple
(LCM)
LISTING METHOD
EXAMPLE
Find the LCM of 8 and 12
Step 1: List the multiples of each number
8, 16, 24, 32
12, 24
Step 2: Circle the smallest number that is in
all the lists.
Step 3: Write the answer LCM = 24
EXAMPLE
Find the LCM of 3, 5, and 6
3, 6, 9, 12, 15, 18, 21, 24, 27, 30,
5, 10, 15, 20, 25, 30,
6, 12, 18, 24, 30,
LCM = 30
Find the LCM of 3 and 5
3, 6, 9, 12, 15
5, 10, 15
Find the LCM of
6, and 9
6, 12, 18
9, 18
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
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?
ITEM
Number per
Pack
Invitations
12
30
10
24
15
5
Balloons
Paper plates
Paper napkins
Plastic cups
Noise makers
3 packs of plates and 2 packs of cups
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?
ITEM
Number per
Pack
Invitations
12
30
10
24
15
5
Balloons
Paper plates
Paper napkins
Plastic cups
Noise makers
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