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Objective - To find the Least Common Multiple (LCM) of numerical and variable expressions and use it to compare and order fractions. LCM - Least Common Multiple - Smallest number that a set of given numbers divides evenly into (the first number that appears in both of the times tables for the numbers. Three ways to find the LCM 1) Make a list of multiples. 2) Use the prime factorizations 3) Use Upside-down Division Make a List of Multiples 1) Find the LCM of 10 and 12. 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 ... 12: 12, 24, 36, 48, 60 LCM = 60 2) Find the LCM of 32 and 40. 32: 32 , 64, 96, 128, 160, 192, 224, 256 ... 40: 40, 80, 120, 160 LCM = 160 Use prime factorization to find the LCM. 18 2 20 2 10 9 3 3 2 3 3 2 5 2 2 5 Select all common factors once. Then select the remaining factors. LCM 2 332 5 LCM 180 Use prime factorization to find the LCM. 45 72 5 9 3 8 3 9 2 4 3 3 2 2 3 3 5 2 2 2 3 3 Select all common factors once. Then select the remaining factors. LCM 3 352 2 2 LCM 360 Using Upside-Down Division to Find the LCM Find the LCM of 48 and 80. 8 Common 2 Factors Once 48 6 3 80 10 5 Remaining Factors LCM 8 2 3 5 LCM 240 Using Upside-Down Division to Find the LCM Find the LCM of 90 and 120. 30 Common Factors Once 90 3 120 4 Remaining Factors LCM 30 3 4 LCM 360 Using Upside-Down Division to Find the LCM 3 Common Factors Once 18x y 3 18 6 2 3 12xy 12 4 2 2 Remember to take every variable to the highest power LCM 3 2 3 2 x y 3 2 LCM 36x y 3 2