Finding the LCM of two expressions

[zolton5971]

Find the least common denominator of 3(2x-2) and x(5x-)5

I wanted to double check this, I got 10 as an answer? If not how would you get the LCD?

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[poissonspot]

Check your answer here: lcm of 3'('2x-2')' and x'('5x-5')' - Wolfram|Alpha

 

[SuperSonic4]

Find the least common denominator of 3(2x-2) and x(5x-)5

I wanted to double check this, I got 10 as an answer? If not how would you get the LCD?

.

Do you mean \(\displaystyle x(5x-5)\)? You're answer should include \(\displaystyle x\) somewhere

The lowest common multiple (LCM) is given by splitting each term into prime factors and multiplying by the highest power of each prime factor. For example to find the LCM of 10 and 15 (it's 30) you'd do

\(\displaystyle 10 = 2 \times 5 \text{ and }\ 15 = 3 \times 5\) so the LCM is given by \(\displaystyle 2 \times 3 \times 5 = 30\)

You can do the same with algebraic fractions but remember to treat any polynomials or variables as prime - after simplifying you have \(\displaystyle 6(x-1)\) and \(\displaystyle 5x(x-1)\)

Can you use the method above to find the LCM?