1. How to find the LCM of two or more numbers (or expressions) Ex: Find the LCM for 40, 30, 36 40 = 23 23 3 30 = 2 35 36 = 2 2 3232 For 2 we select 2323 For 3 we select 3232 For 5 we select 5151 LCM = 2 3 3 2 5 1) For of each number (or expression) get the prime decomposition 2) For each factor in the decompositions select the one with maximum exponent 3) The product of all Answer: LCM = 360

2. Find the LCM for 6x-6, 4x 2 -4, x 2 +2x-3 First get the prime factorization for each polynomial 6x - 6 = 6(x -1) = 2·3 (x -1) 4x 2 - 4 = 4(x 2 -1) = 2 (x +1) (x -1) x 2 + 2x - 3 = 3 (x – 1) (x +1) ( x +3) For 2 we select 2 For 3 we select 3 For x we select x For x +1 we select x +1 For x +3 we select x +3 LCM = 2 2 (3)(x – 1) (x +1) ( x +3) Answer: LCM = 12 (x –1)(x +1)( x +3)

3. We need to find the LCD (LCM for the denominator ) Since 9 = 3232 8 = 2323 24 = 23 23 ·3 So the LCD = 23 23 · 32 32 = 8·9 = 72 Rewriting the fraction with denominator 72 … Find the value of Adding Fractions