SOLUTION: Find the LCM of 21a^2b^6, 3a^4b^8, 14a^5b^8 Thank you

Question 464643: Find the LCM of 21a^2b^6, 3a^4b^8, 14a^5b^8

Thank you
Found 2 solutions by MathLover1, Edwin McCravy:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

Least Common Multiple or :
The smallest (non-zero) number that is a multiple of two or more numbers.

Let's use prime factorization.

Prime factors are , , .

Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!



The other tutor's solution is wrong.

Prime factor them all:

21a�b⁶ = 3�7�a�a�b�b�b�b�b�b

3a⁴b⁸ = 3�a�a�a�a�b�b�b�b�b�b�b�b

14a⁵b⁸ = 2�7�a�a�a�a�a�b�b�b�b�b�b�b�b

 Line those up like this so that only like factors
are lined up vertically. Then draw a line underneath:


  3�7�a�a      �b�b�b�b�b�b
  3  �a�a�a�a  �b�b�b�b�b�b�b�b
2  �7�a�a�a�a�a�b�b�b�b�b�b�b�b
-------------------------------

Bring every factor down on the bottom line

  3�7�a�a      �b�b�b�b�b�b
  3  �a�a�a�a  �b�b�b�b�b�b�b�b
2  �7�a�a�a�a�a�b�b�b�b�b�b�b�b
-------------------------------
2�3�7�a�a�a�a�a�b�b�b�b�b�b�b�b

Multiply all that together and you get:


    42a⁵b⁸

A shorter way is:

1.  Get the LCM of just the coefficients 21,3,and 14, which is 42
2.  use the largest power of each letter that occurs in any one 
    factor.  That's a⁵ and b⁸, for they are the largest
    powers of a and b that appear in any of the 3 original expressions.

Edwin

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