**There is a simple explanation for finding a
common denominator and a more complicated method. Let me give you the simple
explanation first. A common denominator is a number that can be divide evenly by
the other denominators. For example:**

**
3 = 12 **

**
5
20**

**
+ 1
= 5**

**
4 20**

**
17**

**
20**

**20 is a number
that can be divided by 4 and 5 evenly. There is no remainder and therefore
20 is the new denominator. So 20 divided by 5 is 4 and four is then multiplied by 3
to get the new numerator of 12. The same procedure is applied to the 1/4. Is 20
the smallest number that can be divided by 5 and 4 evenly? If so it is the least
common denominator.**

**
Could we have used 40 instead of 20? Yes! But it would not have been the
smallest (least) common denominator and you would have had to reduced the
answer.**

**
3/5 = 24/40**

__ +
1/4 = 10/40 __

**
34/40 dividing 34 and 40 by 2 reduces to 17/20. **

** **

**The
more complicated way to find the least common denominator follows.**

**A common
denominator is a number can be divided by the other denominators evenly. There
will be no remainders. **

** Add 1/8 + 1/3 + 5/6
Find the LCD. Take each denominator and factor it into
its prime factors.**

** So:
8 = 2 x 2 x 2
3 = 3 x 1
6 = 3 x 2**

** Take each prime factor the largest number of times it appears
in any of the numbers and
multiply them together. Your answer is the LCD.**

** Therefore the LCD for the above problem is 2 x 2
x 2 x 3 = LCD = 24.**

** Notice 2 appears in 8 three times and 2 appears
in 6 once. When searching for the LCD
we took 2 three times not four times and 3 once not twice.**

** Lets solve the problem.**

** 1
= 3
**

8 24

** 1
= 8
**

3 24

** 5
= 20
**

+ 6 24

------------------------

31 = 1 7/24

24

**Try this example:
1
Find the LCD for 9, 12 and 14 answer
9
5
12**

** **

** **