1.  Least Common Multiples

2. Multiples  Multiples are the product of a number and any whole number.  LCM- least common multiple- the least multiple common to all numbers.  Find by:  List the multiples  Ex 1: 6 and 9:  6: 6,12,18,24,30, 36,42,48  9: 9,18,27,36, 45,54,63,72,81  LCM: 18

3.  Ex. 2: Find by method 2:  Find the prime factorization of two numbers. Write each prime factor the greatest number of times it occurs for any of the digits.  4,14: 4= 2x2; 14= 2x7: So 2 occurs twice, 7 occurs once:  So 2x2x7=28, 28 is the least common multiple.

4. Uses of LCM  Finding LCM of algebraic terms:  Ex:3  35x^2 and 175xy  35x^2= 5*7*x*x 175 = 7*5*5*x*y  LCM=5*5*7*x*x*y

5. LCD: Least Common Denominator  The LCD will be the LCM of the Denominator:  Ex. 4:  1/12, -3/16, 5/18  Find LCM of 12, 16,18:  12=2*3*2  16=2*2*2*2  18=2*3*3  Multiply 2*2*2*2*3*3=144

6. You can also used the LCD for ALGEBRAIC fractions  Ex. 5: Find LCD for the following  6c/5b; 2c/15b, 7c/25b  5b=5*b  15b=3*5*b  25b=5*5*b  3*5*5*b=75b  LCD is 75b  DO 1-10 in notebook now.