Page 384 - Algebra 1

Math Reasoning
Analyze Why does 11 have only one prime factor?
b. Find the LCM of 11, 12, and 18.
SOLUTION
Write each number as a product of prime numbers.
11 = 11 12 = 2 · 2 · 3 18 = 2 · 3 · 3
The number 2 is a factor of both 18 and 12. The greater number of times it appears is two times in 12, so it will appear two times in the LCM.
2·2
The number 3 is a factor of 12 and 18. The greater number of times it
appears is two times in 18, so it will appear two times in the LCM. 2·2·3·3
Because the number 11 is prime, its only prime factor is 11, so it will appear in the LCM one time.
LCM = 2 · 2 · 3 · 3 · 11 LCM = 396
The LCM of 11, 12, and 18 is 396.
In algebraic expressions, variables are included in the least common multiple. The number of times the variable appears in the least common multiple depends on the number of times it appears in each algebraic expression.
Identifying the LCM of Two Monomials
Find the LCM of 10a2c4 and 15a3c3.
SOLUTION
Write each number as a product of prime numbers.
10a2c4 =2·5·a·a·c·c·c·c
15a3c3 =3·5·a·a·a·c·c·c
In the LCM, the factor 2 will appear one time, 3 will appear one time, and 5 will appear one time.
2·3·5
The greater number of times a appears is three times, so it will also appear three times in the LCM. The greater number of times c appears is four times, so it will appear four times in the LCM.
LCM = 2 · 3 · 5 · a · a · a · c · c · c · c The LCM is 30a3c4.
Finding the Least Common Multiple of Algebraic Expressions
1. Write each expression as a product of prime factors and factors with an exponent of 1.
2. Use every factor of the given numbers as a factor of the LCM. Use each factor the greatest number of times it is a factor of any of the numbers or expressions.
Example
2
Lesson 57 369