Find the least common denominator of each set of fractions. 1 5 , 1 7 , 7 14 \frac15,\frac17,\frac{7}{14}

This problem asks us to find the least common denominator of the fractions. Notice we have the fractions 1/5, 5/7, and 7/14. Now remember, finding the least common denominator is just finding the least common multiple for each denominator of our fraction. Now, we've learned a couple strategies for doing this. We can either try to list out multiples and find our LCD that way, or what we can do is use prime factorization to solve the problem. Now, since there are 3 fractions I'm dealing with here, I want to make sure I actually get to an answer in a surefire way without having to list out too many numbers. So, I'm going to use prime factorization. So, the numbers we're dealing with are 57, and 14. Those are our denominators. Now, the prime factorization for 55 is already a prime number. So, 5 is going to be prime factorization, that's all we have to write out. 7 is also a prime number. Now, 14, on the other hand, breaks down into 2 times 7, and that's everything broken down into prime numbers. Now, our next step is identifying the unique prime factors. I can see we have a 5, we can see we have a 7, then I can see we have a 2 and a 7, but notice that a 7 is already included for one of our denominators, so we don't need to include the other 7 as well, just the 2. We're looking for unique prime factors, things that are unique here. So, in this case, we have 57, and 2. So, to find my LCD that's just going to be the product of 57. And 2 And 5 x 7 x 2, all of that comes out to 70, meaning that 70 is the LCD and the solution to this problem.

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4. Fractions

Finding The Least Common Denominator

Prealgebra & Beginning Algebra

4. Fractions

Finding The Least Common Denominator

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Multiple Choice

Find the least common denominator of each set of fractions.
$one fifth comma one seventh comma 7 over 14$

$70$

$140$

$490$

$35$

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