If you know the center of mass equation to be \sum\nolimits r = \sum\nolimits m_i r_i + ... / \sum\nolimits m_i + ...
then you might wonder what the "easy method" is to find center of mass.
An easy way to solve a problem such as this https://coinsh.red/p/centerofmass.png is to first observe the problem. How is it being supported? How much mass does the beam have in relation to the block?
For this case, lets assume the beam has no mass at all and the block does have a mass of M. The entire beam in terms of length is L and the distance between the block and the nearest support is D.
To find the force of gravity on the supports, think of how the weight would be distributed if it were in the center. Mg/2 would be the magnitude each support would feel if it were in the center. How would that change if it were 1/4 the length away from one support? The closest support would have 3Mg/4 while the other would have Mg/4. How could we derive an equation from this?
If a block is D away from a support, it has the force of L-(D/L) Mg.
The most common method is using center of mass, but this method is useful if the problem is simple enough.