1. Example 1A LCM of Monomials and Polynomials A. Find the LCM of 15a 2 bc 3, 16b 5 c 2, and 20a 3 c 6. 15a 2 bc 3 = 3 ● 5 ● a 2 ● b ● c 3 Factor the first monomial. 16b 5 c 2 = 2 4 ● b 5 ● c 2 Factor the second monomial. 20a 3 c 6 = 2 2 ● 5 ● a 3 ● c 6 Factor the third monomial. LCM= 3 ● 5 ● 2 4 ● a 3 ● b 5 ● c 6 Use each factor the greatest number of times it appears.

2. Example 1A LCM of Monomials and Polynomials Answer: 240a 3 b 5 c 6 = 240a 3 b 5 c 6 Simplify.

3. Example 1B LCM of Monomials and Polynomials B. Find the LCM of x 3 – x 2 – 2x and x 2 – 4x + 4. LCM = x(x + 1)(x – 2) 2 Use each factor the greatest number of times it appears as a factor. x 3 – x 2 – 2x=x(x + 1)(x – 2) Factor the first polynomial. x 2 – 4x + 4=(x – 2) 2 Factor the second polynomial. Answer: x(x + 1)(x – 2) 2

4. Concept

5. Example 2 Monomial Denominators The LCD is 42a 2 b 2. Simplify. Simplify each numerator and denominator. Add the numerators.

6. Example 2 Monomial Denominators Answer:

7. Example 3 Polynomial Denominators Factor the denominators. Simplify. Subtract the numerators. The LCD is 6(x – 5).

8. Example 3 Polynomial Denominators Distributive Property Combine like terms. Simplify. Answer:

9. Example 4 Complex Fractions with Different LCDs The LCD of the numerator is ab. The LCD of the denominator is b. Simplify.

10. Example 4 Complex Fractions with Different LCDs Write as a division expression. Simplify the numerator and denominator. Multiply by the reciprocal of the divisor. Simplify.

11. Example 4 Complex Fractions with Different LCDs Answer:

12. Example 5 Complex Fractions with Same LCD The LCD of all of the denominators is xy. Multiply by Simplify Distribute xy.

13. Example 5 Complex Fractions with Same LCD Answer: