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

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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