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find 2 integers such that they sum to: 1640
and their LCM is: 8400
 one year ago
 one year ago
find 2 integers such that they sum to: 1640 and their LCM is: 8400
 one year ago
 one year ago

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amistre64Best ResponseYou've already chosen the best response.0
my idea is to factor the LCM to create a pool of options
 one year ago

amistre64Best 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
 one year ago

CliffSedgeBest ResponseYou've already chosen the best response.0
Maybe algebra with a quadratic equation?
 one year ago

amistre64Best ResponseYou've already chosen the best response.0
maybe. but number theory methods might be perfered
 one year ago

CliffSedgeBest 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.
 one year ago

PaxPolarisBest ResponseYou've already chosen the best response.1
\[\large x \left( 1640x \right)=8400n\] where n is a natural number
 one year ago

amistre64Best ResponseYou've already chosen the best response.0
hmm, the "n" seems interesting
 one year ago

amistre64Best 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
 one year ago

PaxPolarisBest ResponseYou've already chosen the best response.1
\[x=820 \pm \sqrt {820^28400n}\]
 one year ago

amistre64Best ResponseYou've already chosen the best response.0
i assume the under radical needs to remain 0 or greater?
 one year ago

PaxPolarisBest ResponseYou've already chosen the best response.1
needs to be a perfect square
 one year ago

amistre64Best 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 :)
 one year ago

PaxPolarisBest ResponseYou've already chosen the best response.1
\[\large x=820 \pm 400\sqrt{168121n}\]
 one year ago

amistre64Best ResponseYou've already chosen the best response.0
i think one more condition was such that x and y were both positive values
 one year ago

PaxPolarisBest 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
 one year ago

robtobeyBest 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},
 one year ago
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