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Holt CA Course 1
3-3 Least Common Multiple
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California StandardsCalifornia Standards
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Holt CA Course 1
3-3 Least Common Multiple
Warm UpWrite the prime factorization of each number.
1. 68
2. 225
3. 940Find the greatest common divisor.
4. 27 and 45
5. 32 and 80
22 17
32 52
22 5 47
9
16
Holt CA Course 1
3-3 Least Common Multiple
Number Sense (NS2.4)Number Sense (NS2.4) - Determine - Determine the least common multiplethe least common multiple and the greatest common divisor of whole of whole numbers;numbers; use them to solve problems with fractions (e.g. to find a common denominator to add two fractions or to find the reduced form of a fraction).
California Standards
Holt CA Course 1
3-3 Least Common Multiple
Objective:Objective: You will learn You will learn how to find the least how to find the least common multiple of two or common multiple of two or more whole numbers.more whole numbers.
Holt CA Course 1
3-3 Least Common Multiple
Vocabularymultiple
Least Common Multiple (LCM)
Holt CA Course 1
3-3 Least Common Multiple
The tires on Kendra’s truck should be rotated every 7,500 miles and the oil filter should be replaced every 5,000 miles. What is the lowest mileage at which both services are due at the same time? To find the answer, you can use least common multiples.
Holt CA Course 1
3-3 Least Common MultipleA multiple of a number is a product of that number and a nonzero whole number. Some multiples of 7,500 and 5,000 are as follows:
7,500: 7,500, 15,000, 22,500, 30,000, 37,500, 45,000, . . .5,000: 5,000, 10,000, 15,000, 20,000, 25,000, 30,000, . . .
A common multiple of two or more numbers is a number that is a multiple of each of the given numbers. So 15,000 and 30,000 are common multiples of 7,500 and 5,000.
Holt CA Course 1
3-3 Least Common Multiple
The least common multiple (LCM) of two or more numbers is the common multiple with the least value. The LCM of 7,500 and 5,000 is 15,000. This is the lowest mileage at which both services are due at the same time.
To find the LCM of two or more numbers, use the “Stairs Method!”
Holt CA Course 1
3-3 Least Common Multiple
Find the least common multiple (LCM).
Example 1: Using the “Stairs Method” to Find the LCM
(A) 2, 7 (B) 3, 6, 9
Holt CA Course 1
3-3 Least Common MultipleCheck It Out! Example 2
Find the least common multiple (LCM).
(A) 3, 7 (B) 2, 6, 4
SMART Response QuestionTo set the properties right click and selectSMART Response Question Object->Properties...
Holt CA Course 1
3-3 Least Common Multiple
Find the least common multiple (LCM) of 6060 and 130130.
Example 3: Using the “Stairs Method” to find the LCM
The LCM is 780.
SMART Response QuestionTo set the properties right click and selectSMART Response Question Object->Properties...
Holt CA Course 1
3-3 Least Common MultipleExample 4: Using the “Stairs Method”
to find the LCM
Find the least common multiple (LCM).
14, 35, 49
The LCM is 490.
SMART Response QuestionTo set the properties right click and selectSMART Response Question Object->Properties...
Holt CA Course 1
3-3 Least Common MultipleCheck It Out! Example 5
Find the least common multiple (LCM).
50, 110
The LCM is 550.
SMART Response QuestionTo set the properties right click and selectSMART Response Question Object->Properties...
Holt CA Course 1
3-3 Least Common MultipleCheck It Out! Example 6
18, 36, 54
The LCM is 108.
Find the least common multiple (LCM).
SMART Response QuestionTo set the properties right click and selectSMART Response Question Object->Properties...
Holt CA Course 1
3-3 Least Common Multiple
Mr. Washington will set up the band chairs all in rows of 6 or all in rows of 8. What is the
least number of chairs he will set up?
Example 7: Application
Find the LCM of 6 and 8.
He will set up at least 24 chairs.
SMART Response QuestionTo set the properties right click and selectSMART Response Question Object->Properties...
Holt CA Course 1
3-3 Least Common MultipleCheck It Out! Example 8
Two satellites are put into orbit over the same location at the same time. One orbits the earth every 24 hours, while the second completes an
orbit every 18 hours. How much time will elapse before they are once again over the
same location at the same time? Find the LCM of 24 and 18.
72 hours will elapse before they are over the same location at the same time.
SMART Response QuestionTo set the properties right click and selectSMART Response Question Object->Properties...
Holt CA Course 1
3-3 Least Common Multiple
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Holt CA Course 1
3-3 Least Common MultipleLesson Quiz
Find the least common multiple (LCM).
1. 18, 21
3. 4, 6, 15
5. You are planning a picnic. You can purchase paper plates in packages of 30, paper napkins in packages of 50, and paper cups in packages of 20. What is the least number of each type of package that you can buy and have an equal number of each?
216126
60 16
2. 24, 27
4. 4, 8, 16
10 packages of plates6 packages of napkins15 packages of cups