because all of the denominations are able to divide with it and generate integer numbers for it:
for example:
[tex] \frac{1}{2} x + 3 = \frac{2}{3} x - 1 \\ lcd \: eliminate = 2 \times 3 = 6 \\ [/tex]
so when you multiply 6 to the both sides of this equation we have:
[tex]3x + 18 = 2x - 6[/tex]
so you can find the solution:
x= -18-6=-24
