MHB Finding the LCM of two expressions

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To find the least common denominator (LCD) of the expressions 3(2x-2) and x(5x-5), it's essential to factor each expression. The correct LCD involves identifying the highest powers of each factor present in both expressions. After simplifying, the expressions can be represented as 6(x-1) and 5x(x-1). The final LCD can be calculated by multiplying these factors together, ensuring all variables and polynomials are treated as prime factors in the process.
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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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