Find the lcd for the following fractions: 4/15x^3, 5/ 12x^2 a. 25x^3 b. 60x^3 c. 25x^5 d. 60x^5

For clarity, please enclose the fractional coefficients inside parentheses:

(4/15)x^3, (5/ 12)x^2

Here we have 2 different denominators, 15 and 12.  To get started, factor each:  15 = 3*5, and 12 = 4*5.  Thus, 5 is common to both 15 and 12.  To form the LCD, begin with 5 and include the factors 3 and 4:  5*4*3 = 60.

Multiply both (4/15)x^3 and (5/ 12)x^2 (separately) by this LCD (60), and then divide the results by 60:

(4/15)*60*x^3          (5/12)*60*x^2
and
          60                         60

This results in 

16x^3         25x^2
and
   60              60

These fractions are the same as the original ones, except now they share the same denominator (60).

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