Common Multiples and Problem Solving

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Common Multiplesand Problem Solving
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Teacher Page

• Content Mathematics
• Grade Level 6-10
• Creator Sharon Stadler
• Map Standards

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What is a common multiple?

• a number that is a multiple of two or more
  numbers
• Example
• 5,10,15,20,25,30 are multiples of 5
• 10,20,30,40,50 are multiples of 10
• 6,12,18,24,30 are multiples of 6
• The least common multiple of 5,6,and 10 is 30.
  All three, 5,6 and 10, are factors of 30.

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Find the least common multiple for 8, 12, and 20

• Method 1
• 8 8,16,24,32,40,
• 12 12,24,36,48,60
• 20 20,40,60,80,
• Continue listing multiples until the same number
  is in all of the lists.

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Whats your answer?

• 8 8,16,24,32,40,48,56,64,72,80
• 12 12,24,36,48,60,72,84,96,108
• 20 20,40,60,80,
• WAIT! There must be a faster method!

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Find the least common multiple for 8, 12, and 20

• Method 2
• Factor each of the numbers.
• 8 12 20
• 4 2 4 3 4 5
• 2 2 2 2 2 3 2 2 5
• Multiply any common factors 2 x 2 by all the
  remaining factors 2 x 3 x 5 120

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Check it!

• 8

• 12

10
120
12
10
120
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Find three common multiples.

• 3, 4, 6
• 8, 10, 15

• 3 3,6,9,12,15,18,21,24
• 4 4,8,12,16,20,24,28
• 6 6,12,18,24,30,36
• Three common multiples are
• 12, 24, and 36.
• 82x4 102X5 255x5
• LCM one 2 x one 5 x 4 x 5 200
• Three common multiples are
• 200, 400, and 600.

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Use common multiples to solve the problem.

• Please provide work to support your answer.
• At the grand opening for Blast Buy, every 40th
  customer received a CD. Every 50th customer
  received a CD player. Which was the first
  customer to receive both a CD and a CD player?

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Who gets both?

• Solution
• The customers who will receive a CD are 40, 80,
  120, 160, 200, 240
• The customers who will receive a CD player are
  50, 100, 150, 200
• The200th customer will receive both.

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Use common multiples to solve the problem.

• In June, Lexie will play a soccer game every 4th
  day. And she will have a swim meet every 6th
  day. On which dates in June will she have both a
  soccer game and a swim meet?
• Please show work.

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JUNE
1
1
8
15
22
29
Lexie will both swim and play soccer on the 12th
and the 24th of June.
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Another common multiple problem

• On Blue Ridge Boulevard, at one intersection, the
  traffic light turns red every five minutes, while
  at the intersection three blocks away, that
  light turns red every three minutes. If they are
  both red now, when is the next time they will
  both be red again?