is referring to getting the LCD, least common divisor, namely a value/expression that is divisible by all three factors, but is the least or smallest possible off many.
it doesn't give a good reason why divide by x exactly, but lemme give you another way to get the LCD.
we have three denominators from whom we'd want the LCD, 3, x, and 2x.
3 and x have no factors in common, so we use their product, 3*x or 3x.
now 3x and 2x have x in as a common factor, so we only include it in the LCD once, so the factors for the LCD will end up as 3*x*2 <--- x used only once, because of being common in two of the denominators.
3*x*2 = 6x.
say for example we have three numbers, say they're denominators for example's sake, 15, 6 and 30.
first off we break them out in factors, usually called "prime factoring".
15 = 3 * 5
6 = 2 * 3
30 = 2 * 3 * 5
from (3*5) and (2*3), we see the 3 is repeated, or in both, so we use it once, so the LCD of those two is only 3*5*2, using the 3 only once.
now we need to get the LCD of the one we just found and the remaining 2*3*5.
well, the LCD of the other two is (3*5*2) and the remaining denominator is (2*3*5), but notice, 3 is in both, 2 is in both and 5 is in both, holly guacamole!! since 3, 2 and 5 are repeated, we use them only once, 3*5*2, thus that is the LCD 3*5*2 namely 30.
