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Least Common Multiples S Multiples S Multiples are the product of a number and any whole number. S LCM- least common multiple- the least multiple common to all numbers. S Find by: S List the multiples S Ex 1: 6 and 9: S S S 6: 6,12,18,24,30, 36,42,48 9: 9,18,27,36, 45,54,63,72,81 LCM: 18 S Ex. 2: Find by method 2: S Find the prime factorization of two numbers. Write each prime factor the greatest number of times it occurs for any of the digits. S 4,14: 4= 2x2; 14= 2x7: So 2 occurs twice, 7 occurs once: S So 2x2x7=28, 28 is the least common multiple. Uses of LCM S Finding LCM of algebraic terms: S Ex:3 S 35x^2 and 175xy S 35x^2= 5*7*x*x S LCM=5*5*7*x*x*y 175 = 7*5*5*x*y LCD: Least Common Denominator S The LCD will be the LCM of the Denominator: S Ex. 4: S 1/12, -3/16, 5/18 S Find LCM of 12, 16,18: 12=2*3*2 S 16=2*2*2*2 S 18=2*3*3 S Multiply 2*2*2*2*3*3=144 S You can also used the LCD for ALGEBRAIC fractions S Ex. 5: Find LCD for the following S 6c/5b; 2c/15b, 7c/25b S 5b=5*b S 15b=3*5*b S 25b=5*5*b S 3*5*5*b=75b S LCD is 75b S DO 1-10 in notebook now.
