# Least Common Multiple (LCM) & Greatest Common Division (GCD)

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Least Common Multiple (LCM) & Greatest Common Division (GCD)
Nita Agustin , August 2014 Least Common Multiple (LCM) & Greatest Common Division (GCD)

, 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.

, 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.

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

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 and 23 152=7×23 23=23×1 LCM = 23×7×1=152

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

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

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

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

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

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