Page 385 - Algebra 1

Identifying the LCM of Three Monomials
Find the LCM of 6p2s3, 2m2s2, and 8m3p.
SOLUTION
Write each expression as a product of prime numbers.
6p2s3 =2·3·p·p·s·s·s
2m2s2 =2·m·m·s·s
8m3p =2·2·2·m·m·m·p
In the LCM, the factor 2 will appear three times and the factor 3 will appear one time.
2·2·2·3
No one variable appears in all three expressions. The most the variable m appears is three times. The most the variable p appears is two times. The most the variable s appears is three times.
LCM = 2 · 2 · 2 · 3 · m · m · m · p · p · s · s · s The LCM is 24m3p2s3.
Identifying the LCM of Polynomials
a. Find the LCM of (3x + 1) and (2x + 9).
SOLUTION
The binomials are prime. Their only factors are 1 and themselves. The LCM, then, is the product of the binomials.
The LCM is (3x + 1)(2x + 9).
b. Find the LCM of (7x2 + 21x) and (6x + 18). SOLUTION
Factor each binomial, if possible.
The GCF of the terms in (7x2 + 21x) is 7x. Factor it. (7x2 +21x)=7·x(x+3)
The GCF of the terms in (6x + 18) is 6. Factor it. (6x + 18) = 6(x + 3) = 2 · 3(x + 3)
(x + 3) is a common factor, appearing one time in each binomial. The numbers 2, 3, and 7 are also factors, appearing one time. The variable x is also a factor.
LCM = 2 · 3 · 7 · x(x + 3) The LCM is 42x(x + 3).
Example
3
Hint
To be a factor of the LCM, a number does not need to be a factor of every number in the set. Simply being a factor of one number in the set makes it a factor of the LCM.
Math Reasoning
Justify Explain why the LCM of (3x + 1) and
(2x + 9) is their product.
Example
4
Caution
Be sure to factor all common factors, not just numeric factors.
370 Saxon Algebra 1