Why, when one number is a factor of another, the least common denominator of the numbers is the larger number?

Answer 1

if a number is a factor of another number, that means it can be multiplied by something and go into it evenly. when you are looking for the least common denominator(multiple), you are looking for the smallest number both numbers go into. if one goes into the other one, then that is it because a number can go into itsself (once)

Answer 2

To find the Least Common Denominator:

* Find the Greatest Common Factor of the denominators
* Multiply the denominators together
* Divide the product of the denominators by the Greatest Common Factor.

Example: Find the LCD of 2/9 and 3/12

* Determine the Greatest Common Factor of 9 and 12 which is 3
* Either multiply the denominators and divide by the GCF (9*12=108, 108/3=36)
* OR - Divide one of the denominators by the GCF and multiply the quotient times the other denominator (9/3=3, 3*12=36)

Answer 3

.. just put this in mind.. the largest number usually is the LCD.. why?.. because it is usually not common in set of denominators of a factorable number..ex. you have 1/2+1/3... how do you add this bunch of numbers?.. you just get the least common denominator.. how? you just multiply 2 and 3.. both the denominators of the fraction.. i tell you, it's always like that..sometimes its not only the larger number its the largest.. so the LCD of the fraction would be 6....

Answer 4

Least common denominator is the same as the least common multiple. So, you aren't looking for the least common factor, but the least common multiple.

Example:
2, 4, 6
2= 2,4,6,8,10,12,14,16,18,20....
4= 4,8,12,16,20,24,28,32...
6= 6,12,18,24,30,36,42...
They have the same common multiples, but the least is: 12