Least Common Multiple (LCM) & Greatest Common Division (GCD) Nita Agustin , August 2014 Least Common Multiple (LCM) & Greatest Common Division (GCD) www.ajwmathematics.wordpress.com

, August 2014 Indicator : Dapat menentukan KPK bentuk aljabar suku tunggal. Dapat menentukan FPB bentuk aljabar suku tunggal. Dapat menggunakan KPK untuk menyamakan penyebut aljabar bentuk rasional. Dapat menggunakan FPB untuk menyamakan penyebut aljabar bentuk rasional. www.ajwmathematics.wordpress.com

, August 2014 Definition : Least Common Multiple (LCM) is multiplication product of prime factors of the algebraic forms. Greatest Common Division (GCD) is multiplication product of the same prime factors of the algebraic forms. www.ajwmathematics.wordpress.com

Do you remember? Determine the LCM from: 8 and 64 13 and 7 152 and 23 , August 2014 Do you remember? Determine the LCM from: 8 and 64 13 and 7 152 and 23 Determine the GCD from: 86 and 18 17 and 63 24 and 38 www.ajwmathematics.wordpress.com

Determine the LCM from: 8 and 64 8=2×2×2= 2 3 64=2×2×2×2×2×2= 2 6 LCM = 2 6 2. 13 and 7 13=13×1 7=7×1 LCM = 13×7×1=21 3. 152 and 23 152=7×23 23=23×1 LCM = 23×7×1=152 www.ajwmathematics.wordpress.com

LCM and GCD algebra form a single tribe Determine the LCM and GCD of 15 𝑥 2 and 16𝑥𝑦 15 𝑥 2 =3×5× 𝑥 2 16𝑥𝑦= 2 4 ×𝑥×𝑦 Prime factors is equal to highest rank are 𝑥 2 and 2 4 Prime factors is equal to lowest rank are 𝑥. LCM = 2 4 ×3×5× 𝑥 2 ×𝑦=36000 𝑥 2 𝑦 GCD = 𝑥 www.ajwmathematics.wordpress.com

Determine the GCD from: , August 2014 Determine the GCD from: 86 and 18 86=2×43×1 18=2×3×3×1=2× 3 2 ×1 GCD = 2 2. 17 and 63 17=17×1 63=3×3×7= 3 2 ×7×1 GCD = 1 3. 24 and 38 24=2×2×2×3×1= 2 3 ×3×1 38=2×19×1 www.ajwmathematics.wordpress.com

Using LCM to equalize the denominators of rational algebraic form Equate the denominator from 3 2𝑥𝑦 and 2 𝑦 2 Find the LCM from 2𝑥𝑦 and 𝑦 2 2𝑥𝑦=2×𝑥×𝑦 𝑦 2 = 𝑦 2 Prime factors is equal to highest rank are 𝑦 2 LCM = 2𝑥 𝑦 2 3 2𝑥𝑦 = 3×𝑦 2𝑥𝑦×𝑦 = 3𝑦 2𝑥 𝑦 2 2 𝑦 2 = 2×2×𝑥 2×𝑥× 𝑦 2 = 4𝑥 2𝑥 𝑦 2 www.ajwmathematics.wordpress.com

Using GCD to simplify the algebraic form Simplify the form of 3 𝑝 2 𝑞 12𝑝 𝑞 3 𝑟 Find the GCD from 3 𝑝 2 𝑞 and 12𝑝 𝑞 3 𝑟 3 𝑝 2 𝑞=3× 𝑝 2 ×𝑞 12𝑝 𝑞 3 =3×4×𝑝× 𝑞 3 ×𝑟 Prime factors is equal to lowest rank are 3, 𝑝, and 𝑞 GCD = 3×𝑝×𝑞=3𝑝𝑞 3 𝑝 2 𝑞 12𝑝 𝑞 3 𝑟 = 3 𝑝 2 𝑞 12𝑝 𝑞 3 𝑟 ÷ 3𝑝𝑞 3𝑝𝑞 = 𝑝 4 𝑞 2 𝑟 So the simplify form of 3 𝑝 2 𝑞 12𝑝 𝑞 3 𝑟 is 𝑝 4 𝑞 2 𝑟 www.ajwmathematics.wordpress.com

Algebraic simplify rational shaped composite Simplify the form of 𝑏 2𝑎 − 2𝑎 𝑏 3− 𝑎 𝑏 𝑏 2𝑎 − 2𝑎 𝑏 3− 𝑎 𝑏 = 𝑏 2𝑎 − 2𝑎 𝑏 3− 𝑎 𝑏 × 2𝑎𝑏 2𝑎𝑏 = 𝑏 2 −4 𝑎 2 6𝑎𝑏−2 𝑎 2 Simplify the form of 2𝑎−𝑏 2 𝑎 + 𝑏 2 2𝑎−𝑏 2 𝑎 + 𝑏 2 = 2𝑎−𝑏 2 𝑎 + 𝑏 2 × 2𝑎 2𝑎 = 4 𝑎 2 −2𝑎𝑏 4+𝑎𝑏 www.ajwmathematics.wordpress.com