Finding the Least Common Multiple (LCM) of a Set of Polynomials
Adding and subtracting rational expressions with different denominators is like adding and subtracting fractions with different denominators.
We begin by finding the least common denominator (LCD) of a set of rational expressions.
The LCD of two or more rational expressions is the least common multiple (LCM) of their denominators.We can find the LCM of a set of polynomials in much the same manner that we found the LCM of a set of whole numbers.
Procedure â€” To Find the Least Common Multiple (LCM) of a Set of Polynomials
Step 1 Factor each polynomial.
Step 2 For each factor, list it the greatest number of times it appears in any factorization.
Step 3 Find the product of the factors in the list.
We usually leave the LCM in factored form.
To find the LCM of a set of numbers, say 10, 15, and 18, follow these steps:
Step 1 Write the prime factorization of each number.
10 = 2 Â· 5 15 = 3 Â· 5 18 = 2 Â· 3 Â· 3
Step 2 List each prime factor the greatest number of times it appears in any factorization:
2, 3, 3, 5
Step 3 Multiply the prime factors in the list:
2 Â· 3 Â· 3 Â· 5 = 90
The LCM of 10, 15, and 18 is 90.
Find the LCM of 15xy, 10x2y, and 6xy2.
The LCM of 15xy, 10x2y, and 6xy2 is 30x2y2.
Find the LCM of x2 - 2x, x2 + x - 6, and x2 + 6x + 9
The LCM of x2 - 2x, x2 + x - 6, and x2 + 6x + 9 is x(x - 2)(x + 3)(x + 3).