Transcript least common multiple (LCM)

3-3 Least Common Multiple
California
Standards
NS2.4 Determine the least common
multiple and the greatest common divisor of
whole 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).
Holt CA Course 1
3-3 Least Common Multiple
VOCABULARY CARDS
• Multiple
• 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 Multiple
A 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.
Holt CA Course 1
3-3 Least Common Multiple
Teacher Example 1: Using a List to Find the LCM
Find the least common multiple (LCM).
1A. 2, 7
Multiples of 2: 2, 4, 6, 8, 10, 12, 14
Multiples of 7: 7, 14, 21, 28, 35
The LCM is 14.
List some multiples of
each number.
Find the least value that
is in both lists.
1B. 3, 6, 9
Multiples of 3: 3, 6, 9, 12, 15, 18, 21
Multiples of 6: 6, 12, 18, 24, 30
Multiples of 9: 9, 18, 27, 36, 45
The LCM is 18.
Holt CA Course 1
List some multiples of
each number.
Find the least value that
is in all the lists.
3-3 Least Common Multiple
Student Practice 1:
Find the least common multiple (LCM).
1A. 3, 7
Multiples of 3: 3, 6, 9, 12, 15, 18, 21
Multiples of 7: 7, 14, 21, 28
The LCM is 21.
1B. 2, 6, 4
Multiples of 2: 2, 4, 6, 8, 10, 12, 14
Multiples of 6: 6, 12, 18
Multiples of 4: 4, 8, 12
The LCM is 12.
Holt CA Course 1
List some multiples of
each number.
Find the least value
that is in both lists.
List some multiples of
each number.
Find the least value
that is in all the lists.
3-3 Least Common Multiple
Teacher Example 2: Application
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?
Find the LCM of 6 and 8.
6=23
8=222
The LCM is 2  2  2  3 = 24.
He will set up at least 24 chairs.
Holt CA Course 1
3-3 Least Common Multiple
Student Practice 2:
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.
24 = 2  2  2  3
18 = 2  3  3
The LCM is 2  2  2  3  3 = 72.
72 hours will elapse before they are over the
same location at the same time.
Holt CA Course 1
3-3 Least Common Multiple
Lesson Quiz
Find the least common multiple (LCM).
1. 18, 21
3. 4, 6, 15
126
2. 24, 27
216
4. 4, 8, 16 16
60
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?
10 packages of plates
6 packages of napkins
15 packages of cups
Holt CA Course 1