10. For each pair of polynomials, find the least common multiple.
Example
For each pair of polynomials, find the least common multiple.
a) 16a and 24b
b) 24x4y4 and 6x6y2
c) x2  4 and x2  2x  8
Solution
a) 16a = 2  2  2  2  a
24b = 2  2  2  3  b
The LCM = 2  2  2  2  a  3  b
The LCM is 24  3  a  b, or 48ab
16a is a factor of the LCM
24b is a factor of the LCM

11. b) 24x4y4 = 2  2  2  3  x  x  x  x  y  y  y  y
Example continued
b) 24x4y4 = 2  2  2  3  x  x  x  x  y  y  y  y
6x6y2 = 2  3  x  x  x  x  x  x  y  y
LCM = 2  2  2  3  x  x  x  x  y  y  y  y  x  x
Note that we used the highest power of each factor. The LCM is 24x6y4
c) x2  4 = (x  2)(x + 2)
x2  2x  8 = (x + 2)(x  4)
LCM = (x  2)(x + 2)(x  4)
x2  4 is a factor of the LCM
x2  2x  8 is a factor of the LCM

12. a) b) c) d) e)

13. c.