Download Least Common Multiples Adding Using the LCD

Math 52
6.3 "Least Common Multiples and Denominators"
Objectives:
*
Find the LCM of several numbers by factoring.
*
Add fractions, …rst …nding the LCD.
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Find the LCM of algebraic expressions by factoring.
Least Common Multiples
Finding LCMs:
kTo …nd the LCM, use each factor the greatest number of times that it appears in any one factorization.k
Example 1: (Finding the LCMs)
Find the LCM.
a) 6; 9; 21
b) 24; 36; 40
Adding Using the LCD
Example 2: (Adding using the LCD)
Add, …rst …nding the LCD. Simplify if possible.
1 2
5
+ +
a)
12 6 3
b)
2
5
3
+ +
15 9 20
LCMs of Algebraic Expressions
To …nd the LCM of two or more algebraic expressions, we factor them. Then we use each factor the greatest number of
times that it occurs in any one expression. In Section 6.4, each LCM will become an LCD and will be used to add rational
expressions.
Example 3: (Finding LCMs of algebraic expressions)
Find the LCM.
a) 12x; 16xyz; 8y
b) t2 + 16; t
Page: 1
2; 7
Notes by Bibiana Lopez
Introductory Algebra by Marvin L. Bittinger
c) x2 + 5x + 6; x2
e) 9x3
9x2
d) 10v 2 + 30v; 5v 2 + 35v + 60
4
18x; 6x5
6.3
24x4 + 24x3
f) x5 + 2x4 + x3 ; 2x3
Page: 2
2x; 5x
5
Notes by Bibiana Lopez