Solving Fraction Addition with Denominators 33 and 48: Finding the LCD

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Discussion Overview

The discussion revolves around finding the least common denominator (LCD) for fractions with denominators initially stated as 33 and 48, later corrected to 30 and 48. Participants explore the concept of least common multiple (LCM) in relation to these denominators.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant initially claims the LCD for denominators 33 and 48 is 240 but expresses confusion about how to arrive at this number.
  • Another participant questions whether the term LCD was used correctly, suggesting it may refer to the greatest common divisor (GCD) or least common multiple (LCM), and points out that 240 is not the GCD or LCM of 33 and 48.
  • A later reply clarifies that the denominators were actually 30 and 48, confirming that the LCD is indeed 240 based on their prime factorizations.
  • One participant asserts that the LCD is trivially 1 for all natural numbers and emphasizes that the focus should be on finding the LCM.
  • Another participant agrees that the initial inquiry was about finding the least common multiple of the denominators provided, noting the context of fractions.

Areas of Agreement / Disagreement

Participants generally agree that the discussion is about finding the least common multiple related to the denominators of fractions, but there is some confusion regarding the initial numbers and terminology used.

Contextual Notes

There are limitations in the initial understanding of the denominators, as well as the terminology used (LCD vs. LCM), which may have contributed to the confusion in the discussion.

Holocene
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In adding fractions with denominators of 33 and 48, the LCD is 240.

I don't understand any easy way to arrive at this number.

33 factors out to be : 3 * 11
48 factors out to be: 2 * 2 * 2 * 2 * 3

But from these numbers, none will yeild a product of 240.

What am I doing wrong?
 
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What is the LCD? Did you meand the GCD(Greatest Common Divisor)? Or did you mean the LCM(Least Common Multiple)? As far as I can tell you did nothing wrong, as 240 is neither the gcd nor the lcm of 33 and 48.

EDIT: Oh I guess you meant LCD as in Least Common Denominator, which would be equivalent in this case to the LCM, but still it shouldn't be 240, and you should be able to tell that from the prime factorizations of the three numbers.
 
Last edited:
My mistake!

The denominators of the fractions were 30 (not 33) and 48, and the LCD is in fact 240. I read the problem wrong!

30 = 2 * 3 * 5
48 = 2 * 2 * 2 * 2 * 3

2 * 2 * 2 * 2 * 3 * 5 = 240

Thanks for help. I appreciate it.
 
Last edited:
LCD is is trivially 1 for all natural numbers.

What you are after is LCM, least common multiple.
 
Yes, arildno, he is looking for the least common multiple of the numbers he gave. He did, however, say initially that these were the denominators of given fractions and he was looking for the least common denominator of those fractions.
 

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