FINDING THE LEAST COMMON DENOMINATOR (LCD)

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     =
8           24

1     =    8
3           24

5     =    20
+  6           24
------------------------
31    =   1  7/24
24

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

5
12

3
+  14
________
answer

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