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01Magic Spells Unit
CMath Vo abulary least common multiple (LCM): the smallest common multiple of two or more numbers
1 . Find the least common multiple of two numbers. 1. Have students find multiples, common
multiples, and the least common multiple.
a. 5 and 6 b. 7 and 9
2. Have students use the problem solving
Common multiples of 5 and 6: Common multiples of 7 and 9: method to solve the problems.
30, 60, 90 ... 63, 126 ... 2a.
Understand the Question
The least common multiple The least common multiple Q: What do you need to find?
of 5 and 6:30 of 7 and 9:63 A: If you want to buy an equal number of
pencils and erasers, what is the least
c. 6 and 8 d. 5 and 8 number of pencils and erasers you have
to buy?
Common multiples of 6 and 8: Common multiples of 5 and 8: Q: Read the problem again. What do you
already know?
24, 48 ... 40, 80 ... A: A store sells pencils in packs of 4 and
erasers in packs of 3.
The least common multiple The least common multiple Plan the Process
of 6 and 8:24 of 5 and 8: 40 Q: How will you solve the problem?
A: Find the least common multiple.
2 . Use the least common multiple to solve each problem. Solve the Problem
Refer to 2a. in the textbook.
a. A store sells pencils in packs of 4 and erasers in packs of 3. If you want to Look Back
buy an equal number of each, what is the least number of pencils and Q: Does your answer make sense?
erasers that you have to buy?
Number of pencils you can buy: 4, 8, 12, 16, 20, 24 ...
Number of erasers you can buy: 3, 6, 9, 12, 15, 18 ...
The LCM of 3 and 4: 12
You have to buy 12 pencils and 12 erasers.
b. Ricky wants to make a square using tiles that are 12 inches wide and
21 inches long. What is the length of the side of the smallest square that
Ricky can make using these tiles?
Length of the width: 12, 24, 36, 48, 60, 72, 84 ...
Length of the other side: 21, 42, 63, 84 ...
The LCM of 12 and 21: 84 9
The length of the side of the smallest square that Ricky can make is 84 inches.
1. Magic Spells
Problem: From station A, the train departs every 30 minutes and the subway departs every 12 minutes. If
both the train and subway depart at 9 am, find the next time both the train and subway will depart
at the same time.
Solution: Step 1: Train departure: Since the train departs every 30 minutes, find the multiples of 30.
30, 60, 90, 120, 150, 180, …
Step 2: Subway departure: Since the subway departs every 12 minutes, find the multiplies 12.
12, 24, 36, 48, 60, 84,….
Step 3: The LCM of 30 and 12: 60
The next time both the train and subway will depart together is 60 minutes after 9 am, which is
10 am.
Answer: 10 am
5A Unit 01 011
CMath Vo abulary least common multiple (LCM): the smallest common multiple of two or more numbers
1 . Find the least common multiple of two numbers. 1. Have students find multiples, common
multiples, and the least common multiple.
a. 5 and 6 b. 7 and 9
2. Have students use the problem solving
Common multiples of 5 and 6: Common multiples of 7 and 9: method to solve the problems.
30, 60, 90 ... 63, 126 ... 2a.
Understand the Question
The least common multiple The least common multiple Q: What do you need to find?
of 5 and 6:30 of 7 and 9:63 A: If you want to buy an equal number of
pencils and erasers, what is the least
c. 6 and 8 d. 5 and 8 number of pencils and erasers you have
to buy?
Common multiples of 6 and 8: Common multiples of 5 and 8: Q: Read the problem again. What do you
already know?
24, 48 ... 40, 80 ... A: A store sells pencils in packs of 4 and
erasers in packs of 3.
The least common multiple The least common multiple Plan the Process
of 6 and 8:24 of 5 and 8: 40 Q: How will you solve the problem?
A: Find the least common multiple.
2 . Use the least common multiple to solve each problem. Solve the Problem
Refer to 2a. in the textbook.
a. A store sells pencils in packs of 4 and erasers in packs of 3. If you want to Look Back
buy an equal number of each, what is the least number of pencils and Q: Does your answer make sense?
erasers that you have to buy?
Number of pencils you can buy: 4, 8, 12, 16, 20, 24 ...
Number of erasers you can buy: 3, 6, 9, 12, 15, 18 ...
The LCM of 3 and 4: 12
You have to buy 12 pencils and 12 erasers.
b. Ricky wants to make a square using tiles that are 12 inches wide and
21 inches long. What is the length of the side of the smallest square that
Ricky can make using these tiles?
Length of the width: 12, 24, 36, 48, 60, 72, 84 ...
Length of the other side: 21, 42, 63, 84 ...
The LCM of 12 and 21: 84 9
The length of the side of the smallest square that Ricky can make is 84 inches.
1. Magic Spells
Problem: From station A, the train departs every 30 minutes and the subway departs every 12 minutes. If
both the train and subway depart at 9 am, find the next time both the train and subway will depart
at the same time.
Solution: Step 1: Train departure: Since the train departs every 30 minutes, find the multiples of 30.
30, 60, 90, 120, 150, 180, …
Step 2: Subway departure: Since the subway departs every 12 minutes, find the multiplies 12.
12, 24, 36, 48, 60, 84,….
Step 3: The LCM of 30 and 12: 60
The next time both the train and subway will depart together is 60 minutes after 9 am, which is
10 am.
Answer: 10 am
5A Unit 01 011
