I don't know if this is the correct forum but...
Suppose you had a difference of fractions 1/4 - 1/6
You could get the LCD by factoring each denominator. For 4 you would have (2,2) for 6 you would have (2,3). This gives 12 as the LCD.
You would then multiply the numerator of 1/4 by 3, which is the factorization of 6 (2,3) not including the factor that is a factor of 4, namely 2. This gives 3/12
This prime number (3) is the same as dividing the LCD by the original denominator: 12/4 = 3
I hope this makes sense.
Is there a mathematical principle or law that describes this?