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amistre64
Group Title
find 2 integers such that they sum to: 1640
and their LCM is: 8400
 2 years ago
 2 years ago
amistre64 Group Title
find 2 integers such that they sum to: 1640 and their LCM is: 8400
 2 years ago
 2 years ago

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amistre64 Group TitleBest ResponseYou've already chosen the best response.0
my idea is to factor the LCM to create a pool of options
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.0
8400 = 84*100 = 84*2*2*5*5 = 2*2*3*7*2*2*5*5 2*2*2*2*3*5*5*7, therefore 2 2*2 2*2*2 2*2*2*2 2*2*2*2*3 2*2*2*2*3*5 2*2*2*2*3*5*5 2*2*2*2*3*5*5*7 etc ... but that does seem like a long way around it
 2 years ago

CliffSedge Group TitleBest ResponseYou've already chosen the best response.0
Maybe algebra with a quadratic equation?
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.0
maybe. but number theory methods might be perfered
 2 years ago

CliffSedge Group TitleBest ResponseYou've already chosen the best response.0
Might want to use optimization methods from calculus too to minimize the coefficients. Yes, it does seem like a number theory issue, but algebra is always my starting point for solving unknowns.
 2 years ago

PaxPolaris Group TitleBest ResponseYou've already chosen the best response.1
\[\large x \left( 1640x \right)=8400n\] where n is a natural number
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.0
hmm, the "n" seems interesting
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.0
on the test i just ended up using the y= on my ti83 y1 = 1640x y2= lcm(x,1640x) then searched thru that table till i found y2 = 8400
 2 years ago

PaxPolaris Group TitleBest ResponseYou've already chosen the best response.1
\[x=820 \pm \sqrt {820^28400n}\]
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.0
i assume the under radical needs to remain 0 or greater?
 2 years ago

PaxPolaris Group TitleBest ResponseYou've already chosen the best response.1
needs to be a perfect square
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.0
lol, yeah i spose that would have to be a major caveat seeing the x needs to be an integer :)
 2 years ago

PaxPolaris Group TitleBest ResponseYou've already chosen the best response.1
\[\large x=820 \pm 400\sqrt{168121n}\]
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.0
i think one more condition was such that x and y were both positive values
 2 years ago

PaxPolaris Group TitleBest ResponseYou've already chosen the best response.1
sorry, \[\large x=820 \pm \sqrt{400(168121n)}\]\[\large x=820 \pm 20\sqrt{168121n}\] and n is the GCF of x and y
 2 years ago

robtobey Group TitleBest ResponseYou've already chosen the best response.0
240 + 1400 = 1640, LCM[240, 1400] = 8400 Used the following small program and fed it to Mathematica. Table[{n, LCM[n, 1640  n] == 8400}, {n, 820}] Part of the Output: {233, False}, {234, False}, {235, False}, {236, False}, {237, False}, \ {238, False}, {239, False}, {240, True}, {241, False}, {242, False}, \ {243, False}, {244, False},
 2 years ago
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