Question 309282
Well a quick and easy way to get a common multiple of 2 (or more) numbers is to simply multiply them. For instance, a common multiple of 17 and 5 is 17*5=85



In this case, a common multiple between 6 and 12 is 6*12=72. It turns out that the numbers that share the common multiple will go into that common multiple. Ie {{{72/6=12}}} and {{{72/12=6}}}. What this means is that you can effectively clear out the denominators of the fractions leaving you with integer terms.



For instance, multiply 72 by {{{3x/6}}} to get {{{72(3x/6)=(72*3x)/6=216x/6=36x}}}. In the given problem, the only difference is that 36x is really -36x. So instead we must multiply both sides by -72.



Another quick way to realize that -72 is the magic number is to look at the right side. This side already has an integer which will make life easier for us. Take the number 7 and multiply it by some unknown number 'k' to get 7k. This is now equal to the new right side of -504. Set them equal to get 7k=-504. The task now is to solve the equation 7k=-504. Sure enough, solving the equation will get us k=-72 which is the number we're looking for.