## Primary Divisonal 2012/4

Problem for Primary Group from Divisional Mathematical Olympiad will be solved here.
Forum rules
Please don't post problems (by starting a topic) in the "Primary: Solved" forum. This forum is only for showcasing the problems for the convenience of the users. You can post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
Phlembac Adib Hasan
Posts: 1016
Joined: Tue Nov 22, 2011 7:49 pm
Location: 127.0.0.1
Contact:

### Primary Divisonal 2012/4

The LCM of two numbers is \$7\$ times of their GCD. If the sum of the numbers is \$56\$, find their GCD.
Welcome to BdMO Online Forum. Check out Forum Guides & Rules

tanmoy
Posts: 288
Joined: Fri Oct 18, 2013 11:56 pm
Location: Rangpur,Bangladesh

### Re: Primary Divisonal 2012/4

The GCD is \$7\$.
Soppose,the numbers are \$a\$ and \$b\$ and suppose the GCD of the numbers are \$x\$.So,\$a=xa_{1}\$ and \$b=xb_{1}\$ for some integers \$a_{1}\$ and \$b_{1}\$ so that the GCD of \$a_{1}\$ and \$b_{1}\$ is \$1\$
\$\therefore\$ \$7x=xa_{1}b_{1}\$.Or,\$a_{1}b_{1}=7\$.So,one of \$a_{1}\$ and \$b_{1}\$ is \$1\$ and other is \$7\$.
Now,\$xa_{1}+xb_{1}=56\$
Or,\$x(a_{1}+b_{1})=56\$
Or,\$8x=56\$
Or,\$x=7\$ "Questions we can't answer are far better than answers we can't question"