1. Least Common Multiple LCM 2 Methods

2. Name the first six multiples of 6
6, 12, 18, 24, 30, 36

3. Name the first six multiples of 5
5, 10, 15, 20, 25, 30

4. Common Multiple
A Common Multiple is a number that is a multiple of two numbers.
Here are common multiples for the numbers 4 and 10
4 = 4, 8, 12, 16, 20, 24
10 = 10, 20, 30, 40, 50,

5. Least Common Multiple
LCM -
Smallest
number that a set of given numbers divides
evenly into.
Least Common Multiple -
It is useful to know how to do this so you can find a common denominator when adding or subtracting fractions.
THERE ARE TWO WAYS TO FIND LCM

6. Least Common Multiple Method # 1
TO FIND THE LCM OF TWO NUMBERS
List the multiples of both numbers
Find the least multiple that
both numbers have in common.

7. Least Common Multiple Method # 1
Make a List of Multiples
Find the LCM of 10 and 12.
10: 10
, 20
, 30
, 40
, 50
, 60
, 70
, 80
, 90
, 100
...
12: 12
, 24
, 36
, 48
, 60
LCM = 60

8. Least Common Multiple Method # 1
Make a List of Multiples
Find the LCM of 32 and 40.
32: 32
, 64
, 96
, 128
, 160
, 192
, 224
, 256
...
40: 40
, 80
, 120
, 160
LCM = 160

9. What is the Least Common Multiple of 4 & 10
4 = 4, 8, 12, 16, 20, 24
10 = 10, 20, 30, 40, 50,

10. What is the Least Common Multiple of 6 & 8
6 = 6, 12, 18, 24, 30, 36
8 = 8, 16, 24, 32, 40, 48

11. What is the Least Common Multiple of 3 & 9
3 = 3, 6, 9, 12, 15, 21,
9 = 9, 18, 27, 36, 45, 54

12. Method #1 is easy to do!
Method #1 is a good method if both of your numbers are really small.
What if you have really large numbers? It might take too long to keep listing multiples until you find a common multiple.
SO HERE IS METHOD # 2

13. Least Common Multiple Method # 2
1) Write the prime factorization of each number.
Select all common factors ONCE.
3) Then select the remaining factors and multiply.

14. Least Common Multiple Method # 218 20 2 9 2 10 3 3 2 5
Select all common factors once.
Then select the remaining factors.

15. Least Common Multiple Method # 245 72 5 9 8 9 3 3 2 4 3 3 2 2
Select all common factors once.
Then select the remaining factors.

16. Least Common Multiple Method # 2
Find the LCM of 48 and 80. 2
Common
Factors
Once 2 2 2
Remaining
Factors

17. LCM Prime Factorization Method # 2
1) List the prime factorization to find the LCM. 18 20 2 9 2 10 3 3 2 5
2) Select all common factors once.
3) Select all remaining factors, and multiply.
LCM = 180
LCM =

18. Try these Find LCM of 15 and 10 Find LCM of 21 and 14
Find the LCM 60 and 75