1. Least Common Denominator
… the Least Common Multiple of the denominators…

2. Introductory Video

3. What is a Denominator?
The denominator is the _______ _______ in a fraction.
It shows how many equal parts the item is divided Into.

4. What is a Common Denominator?
When the denominators of two or more fractions are the _____, they have ________ ____________.

5. What is a Least Common Denominator?
It is the ________ of all the common denominators.

6. Why Do We Want Common Denominators?
Because we ____ ____ fractions with different denominators.
Before we can add them, we must make the denominators the same.

7. Finding a Common Denominator
But what should the new denominator be?
One simple answer is to multiply the two _____________together. __ x __ = ___
So instead of 3 and 6 slices, we make both have 18 slices.
They now have common denominators (but not the least common denominator.)

8. Least Common Denominator

9. Least Common Denominator
So let’s try using it! We want both fractions to have 6 slices:

10. The Last Step… …is to ___________ the fraction, if possible.
In this case, is simpler as 1 2

11. Least Common Denominator
And that is what the Least Common Denominator is all about.
It let’s us add (or subtract) fractions with the least number of slices.

12. What Did We Do?
We found the ___________________of the denominators (which is called the least common ______________)
We changed each fraction (using _______________) to make their denominators the same as the least common denominator
Then we _________ (or subtracted) the fractions.

13. Least Common Denominator
And that is what the Least Common Denominator is all about.
It let’s us add (or subtract) fractions with the least number of slices.

14. What Did We Do?
We found the ________________________ of the denominators (which is called the least common ____________)
We changed each fraction (using ___________ _________) to make their denominators the same as the least common denominator
Then we ________ (or subtracted) the fractions.

15. Least Common Multiple (LCM)
… Also called the Least Common Denominator …

16. LCM Defined
The Least Common Multiple (LCM) of two numbers is the ____________ number that can be ___________ by both.
It can be used to find the Lowest Common Denominator (LCD) when adding or subtracting ________________.
Don’t let the “least” in the name fool you – the LCM will be no smaller than the _____________ of the numbers.
HINTS:
LEAST – lowest or smallest
COMMON – something shared or in common.
MULTIPLE – what you get when you multiply.

17. How to Find the LCM

18. Make Denominators the Same for 1 6 and 7 15
NOTE: What we do to the bottom of the fraction, we must also do to the top.
For the 1st fraction we can multiply top and bottom by 5 to get a denominator of 30
Multiply the top and bottom of the 2nd fraction by 2 to get a denominator of 30

19. Now We Can Add
= 19 30
19 is a _______ number so it has only 1 and itself as factors.
The fraction is as _______ as it can be, so that is the answer.

20. One More Example Find the LCM of 4 and 6.
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, …
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, ...
Since 12, 24, 36, 48…can all be divided by 4 and 6, each of them is a common multiple and could be used as a common denominator for 4 and 6.
The _________ common multiple is 12, therefore it is the Least Common Multiple (LCM) of 4 and 6.

21. You Can Also Use Prime Factorization to Find LCM
To find the Least Common Multiple of 10 and 12:
Count the ____________ number of times each factor appears in either quantity.
The _____________ of those factors is the Least Common Multiple (LCM)

22. Some Other Ways to Find LCM
Usually you can find the Least Common Multiple fairly easily by experimentation.
Start with the larger number:
Will the other number divide into it? If so, you have the L.C.M.
If not: What is the next multiple of the larger number?
Is IT divisible by the other number?
Continue until you find a number that is divisible by both numbers.
If they share no common factors (other than one) then the Lowest Common Multiple will be the product of the two numbers.

23. Some Other Ways to Find LCM
For example the L.C.M. of 5 and 8 is 40 
Since the only common factor is one, just multiply the numbers:  
5 x 8 = 40. 
Find the Lowest Common Multiple (L.C.M.) of 6 and 12. 
Will 6 go into 12?
Yes.... L.C.M.= 12 
Find the Lowest Common Multiple (L.C.M.) of 6 and 10.          Will 6 go into 10?   No.... Next Multiple 2*10 = 20          Will 6 go into 20?   No.... Next Multiple 3*10 = 30          Will 6 go into 30?   Yes.... L.C.M. = 30