Finding the LCM of two expressions

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The discussion focuses on finding the least common denominator (LCD) of the expressions 3(2x-2) and x(5x-5). The correct approach involves identifying the lowest common multiple (LCM) by factoring each expression into its prime components. The LCM of the simplified forms, 6(x-1) and 5x(x-1), is calculated by multiplying the highest powers of each factor, resulting in an LCM of 30x(x-1). The initial claim of 10 as the answer is incorrect, as it does not account for the variable factors present in the expressions.

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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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zolton5971 said:
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 $$x(5x-5)$$? You're answer should include $$x$$ 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

$$10 = 2 \times 5 \text{ and }\ 15 = 3 \times 5[/math] so the LCM is given by $$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 $$6(x-1)$$ and $$5x(x-1)$$

Can you use the method above to find the LCM?
 

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