LCM of 22x32x4 and 23x3: Explained

[prasadini]

The Lowest Common Multiple of 22x32x4 and 23x3

 

[Greg]

Do you have any ideas on how this problem may be approached?

 

[prasadini]

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

 

[dsuhaimi]

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??

 

[Fermat1]

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.

 

[MarkFL]

The Lowest Common Multiple of 22x32x4 and 23x3

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

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

\(\displaystyle 23\cdot3=3\cdot23\)

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 $N$:

\(\displaystyle N=2^8\cdot3\cdot11\cdot23=194304\)

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