Lesson 5-3 for exercise sets. &KDSWHU 3UDFWLFH $FWLYLWLHVFind the LCM of each set of numbers. List the multiples, or use prime factorization.
1.5, 7 2.4, 5, and 10 3.6, 9, and 12 4.2, 3, 4, and 8Find the LCD of each set of fractions. List the multiples, or use prime factorization.- and 6. , , and 7. , , and 8. and
9.Discuss and Write If one number is a factor of the other, what can
you say about the least common multiple of the two numbers?3
83
59
141
84
75
83
42
33
101
6Find the LCM of 6, 8, and 9.Method 1 List the Multiples- List the multiples of each number.
Multiples of 6: 6, 12, 18, 24, 30,
36, 42, 48, 54, 60, 66, 72,...
Multiples of 8: 8, 16, 24, 32, 40,
48, 56, 64, 72,...
Multiples of 9: 9, 18, 27, 36, 45,
54, 63, 72,... - Identify the least multiple that is
common to the three numbers: 72
So the LCM of 6, 8, and 9 is 72.
1
You can use the same methods for finding the LCM to find the
least common denominator (LCD)of two or more fractions.
The is the least common multiple
of the denominators of two or more fractions.
To find the LCD of , , and^3845207 :least common denominator (LCD)Method 1 List the Multiples- List the multiples of each denominator until
you find a multiple that is common to all
three denominators.
Multiples of 8: 8, 16, 24, 32, 40
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40
Multiples of 20: 20, 40 - Identify the least multiple that is common
to the three numbers: 40
Since the LCM of 8, 5, and 20 is 40, the LCD of , , and^3845207 is 40.Method 2 Use Prime Factorization- Write the prime factorization of each
denominator. Then find the greatest
number of times each factor appears in
any prime factorization.
8 2 • 2• 2
5 5
20 2 • 2 • 5 - Multiply the factors: 2• 2• 2• 5 40
Method 2 Use Prime Factorization- Find the prime factorization
of each number.
6 2 • 3
8 2 • 2• 2or2^3
9 3 • 3 or 3^2 - Write each base once, using the
greatest exponent.
23 • 3^2 72
So the LCM of 6, 8, and 9 is 72.