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Stuck! Pls help quick
Posted: Wed Dec 21, 2016 11:45 pm
by ahsaf
I am stuck with this problem. Please help me. 
The LCM of two numbers is $7$ times of their GCD. If the sum of numbers is $392$, then find out their GCD.
Re: Stuck! Pls help quick
Posted: Fri Dec 23, 2016 4:00 am
by SMMamun
Where are you stuck? In this type of problem, it's convenient to start on GCD:
Let GCD be $g$ and the two numbers be $gx$ and $gy$, in which $x$ and $y$ are co-primes.
$gxy=7g$
$xy=7$
Think about what the values of $(x,y)$ could be.
Then you have just to solve
$gx+gy=392$
Re: Stuck! Pls help quick
Posted: Sun Jan 15, 2017 7:54 pm
by zarif
Let GCD be g and the two numbers be ga,gb.
LCM is gab and gab=7g;ab=7
again,ga+gb=g(a+b)=392
let a be 7 and b be 1
then 8g=392;g=49
the 1st number is 343 and 2nd is 49