Answer:
probably FALSE
Step-by-step explanation:
The least common denominator (LCD) of two fractions is the least common multiple (LCM) of their denominators.
One of the ways to find the LCM of numbers is to factor them, then multiply the highest powers of each of the unique factors. Using this method makes your statement FALSE.
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Another way to find the LCM is to multiply the numbers and divide that product by their greatest common denominator (GCD). Again, finding the GCD can involve factoring, as it is the product of all of the common factors of the numbers.
However, Euclid's algorithm is a method of finding the GCD that does not involve factoring. That is, it is entirely possible to find the LCM of two numbers without doing any factoring, per se. (Though, finding a divisor could be considered factoring.) Using this method makes your statement TRUE.
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Our guess is that the desired answer is FALSE. Some methods of finding the LCD do involve factoring.
