MHB LCM of 22x32x4 and 23x3: Explained

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The discussion focuses on finding the Lowest Common Multiple (LCM) of the expressions 22x32x4 and 23x3. Participants suggest starting with the prime factorization of both numbers, leading to the conclusion that the LCM is calculated by taking the highest powers of each prime factor. The prime factorization results in the LCM being 194304, as the two expressions are co-prime. There is some confusion regarding the value of 144 as a potential multiple, which is clarified through the factorization process. Ultimately, the correct LCM is established as 194304.
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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
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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