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A: Simple question pertaining to LCM

lab bhattacharjeeLet the numbers be $2x,3x\implies $ GCD $=x$ As you have rightly identified , the LCM is $\frac{\text{ Product}}{\text{ GCD }}=6x\implies 6x=48\implies x=8$

Mr.Anubis
Mr.Anubis
Can you please forget the formula for the moment, go the analyzing way?
lab bhattacharjee
lab bhattacharjee
@Mr.Anubis, lcm $(2x,3x)=x\cdot$lcm$(2,3)=6x,$ right?
Mr.Anubis
Mr.Anubis
How did you take $x$ in (2x,3x)=x⋅lcm(2,3) simply out I am wondering . I am looking for concept which I am missing
lab bhattacharjee
lab bhattacharjee
@Mr.Anubis, consider real example with different combinations when $2,3$ divide $x$ and when they don't divide.
Proof (vii) of Article $9.1.12$ in bookos.org/book/1500438
Mr.Anubis
Mr.Anubis
Can you tell where my analysis which I posted in my answer is wrong?
I am about to cry really
lab bhattacharjee
lab bhattacharjee
15:53
" since LCM contains 31 , it must come from either number" is false
Mr.Anubis
Mr.Anubis
why is that?
lab bhattacharjee
lab bhattacharjee
it must come from at least one of the numbers
what you said is true for GCD
Mr.Anubis
Mr.Anubis
aah
but I am still confused , how to tackle the problem using just analysis
lab bhattacharjee
lab bhattacharjee
what is the problem using LCM * GCD = product?
Mr.Anubis
Mr.Anubis
I don't get close to question and concept
lab bhattacharjee
lab bhattacharjee
15:56
example lcm (2*12,3*12)= 12*6
lcm(2*7,3*7)= 7*6
Mr.Anubis
Mr.Anubis
@labbhattacharjee what is this proof?
lab bhattacharjee
lab bhattacharjee
I'm adding to the answer
Mr.Anubis
Mr.Anubis
Thanks a lot, I really appreciate the help
lab bhattacharjee
lab bhattacharjee
please fidn the edited answer
 
2 hours later…
lab bhattacharjee
lab bhattacharjee
18:01
" since LCM contains 31 , it must come from either number" should be from at least one of the numbers
Also "it's obvious 2^4 comes from other number which is 2x" not fully correct as $3x$ may contain $2^m$ where $0<=m<=4$

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