A community for students.
Here's the question you clicked on:
 0 viewing
amistre64
 3 years ago
find 2 integers such that they sum to: 1640
and their LCM is: 8400
amistre64
 3 years ago
find 2 integers such that they sum to: 1640 and their LCM is: 8400

This Question is Closed

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

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.08400 = 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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Maybe algebra with a quadratic equation?

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Might 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.

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

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.0hmm, the "n" seems interesting

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.0on 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

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

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

PaxPolaris
 3 years ago
Best ResponseYou've already chosen the best response.1needs to be a perfect square

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

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

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

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0240 + 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},
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.