SOLUTION: LCM 35x²+105x and 5x²+20x+15

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Question 233368: LCM 35x²+105x and 5x²+20x+15
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
LCM of 35x%5E2%2B105x and 5x%5E2%2B20x%2B15

To find an LCM you must know the factors. So we start by factoring:
35x%5E2%2B105x+=+35x%28x+%2B+7%29+=+5%2A7%2Ax%2A%28x%2B3%29
5x%5E2%2B20x%2B15+=+5%28x%5E2+%2B4x+%2B+3%29+=+5%28x%2B3%29%28x%2B1%29
The LCM is the product of all these factors using the highest exponent on each common factor:


Note that the common factors, 5 and (x+3), were used only once. If, for example, we had had (x+3)^2 in one factorization and (x+3) in the other, then we would use (x+3)^2 (the higher exponent) in the LCM.