Find two numbers a,b such us: a+b=5432 & LCM[a,b]=223020

*To*: mathgroup at smc.vnet.net*Subject*: [mg122153] Find two numbers a,b such us: a+b=5432 & LCM[a,b]=223020*From*: dimitris <dimmechan at yahoo.com>*Date*: Sun, 16 Oct 2011 16:45:09 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

This is taken from the recent book (2010): " Mathematica: A Problem- Centered Approach" by R. Hazrat. "The sum of two positive integers is 5432 and their least common multiple is 223020. Find the numbers." A solution: Do[If[LCM[i, 5432 - i] == 223020, Print[i, " ", 5432 - i]], {i, 1, 2718}] 1652 3780 I wonder if we can solve the system of equations: a+b==5432&&LCM[a,b]==223020 using codes that contain built in functions like Reduce. I guess this is not a trivial one because the so much powerful Reduce itself fails In[1]:= Reduce[{a + b == 5432, LCM[a, b] == 223020}, {a, b}, Integers] During evaluation of In[1]:= Reduce::nsmet:This system cannot be solved with the methods available to Reduce. >> Out[1]= Reduce[{a + b == 5432, LCM[a, b] == 223020}, {a, b}, Integers] Any ideas? Dimitris

**Follow-Ups**:**Re: Find two numbers a,b such us: a+b=5432 & LCM[a,b]=223020***From:*János Löbb <janos@lobb.com>

**Re: Find two numbers a,b such us: a+b=5432 & LCM[a,b]=223020***From:*Sseziwa Mukasa <mukasa@gmail.com>