LCM of 22x32x4 and 23x3: Explained

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Discussion Overview

The discussion revolves around finding the Lowest Common Multiple (LCM) of the expressions 22x32x4 and 23x3. Participants explore different approaches to solve the problem, including prime factorization and numerical reasoning.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • Some participants inquire about possible approaches to determine the LCM of the two expressions.
  • One participant suggests that the LCM can be calculated using prime factorization, providing a detailed breakdown of the factors involved.
  • Another participant questions the validity of 144 being a multiple of 22x32x4, expressing confusion over the relationship between the two values.
  • There are repeated mentions of two potential answers, 144 and 24 x 32, without clear justification for their correctness.
  • A participant emphasizes the importance of demonstrating thought on the problem before seeking help.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct answer or the validity of the proposed solutions. Multiple competing views and uncertainties remain regarding the calculations and interpretations of the LCM.

Contextual Notes

Some assumptions about the definitions of multiples and the calculations involved are not explicitly stated, leading to potential misunderstandings. The discussion includes unresolved mathematical steps and varying interpretations of the problem.

Who May Find This Useful

This discussion may be of interest to individuals seeking to understand methods for calculating the LCM, particularly through prime factorization, as well as those interested in the nuances of mathematical reasoning and problem-solving approaches.

prasadini
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The Lowest Common Multiple of 22x32x4 and 23x3
 
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Do you have any ideas on how this problem may be approached?
 
greg1313 said:
Do you have any ideas on how this problem may be approached?

There is 2 answer
(a) 144 (e) 24 𝑋 32 How can i get this answer
 
prasadini said:
There is 2 answer
(a) 144 (e) 24 𝑋 32 How can i get this answer

Sorry for dumb question, but how is 144 a multiple of 22x32x4? isn't 144<22x32x4??
 
prasadini said:
There is 2 answer
(a) 144 (e) 24 𝑋 32 How can i get this answer

You need to start showing you have at least thought about the problem before posting.
 
prasadini said:
The Lowest Common Multiple of 22x32x4 and 23x3

I would begin by writing the prime factorizations of both numbers:

$$22\cdot32\cdot4=(2\cdot11)(2^5)(2^2)=2^8\cdot11$$

$$23\cdot3=3\cdot23$$

Now, combine the prime factors from both, using the higher power of each prime factor found in either, to get the LCM, which we'll call $N$:

$$N=2^8\cdot3\cdot11\cdot23=194304$$

Since the two given numbers are co-prime, we find their LCM to simply be their product. :D
 

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