Transcript Objective - To find the Least Common Multiple (LCM) of numerical

Objective - To find the Least Common Multiple
(LCM) of numerical and variable expressions
and use it to compare and order fractions.
LCM - Least Common Multiple - Smallest
number that a set of given numbers divides
evenly into (the first number that appears in
both of the times tables for the numbers.
Three ways to find the LCM
1) Make a list of multiples.
2) Use the prime factorizations
3) Use Upside-down Division
Make a List of Multiples
1) 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
2) Find the LCM of 32 and 40.
32: 32 , 64, 96, 128, 160, 192, 224, 256 ...
40: 40, 80, 120, 160
LCM = 160
Use prime factorization to find the LCM.
18
2
20
2 10
9
3
3
2  3 3
2
5
2  2 5
Select all common factors once.
Then select the remaining factors.
LCM  2 332 5
LCM  180
Use prime factorization to find the LCM.
45
72
5
9
3
8
3
9
2 4 3 3
2 2
3 3 5
2  2 2 3 3
Select all common factors once.
Then select the remaining factors.
LCM  3 352 2 2
LCM  360
Using Upside-Down Division to Find the LCM
Find the LCM of 48 and 80.
8
Common
2
Factors
Once
48
6
3
80
10
5
Remaining
Factors
LCM  8  2  3  5
LCM  240
Using Upside-Down Division to Find the LCM
Find the LCM of 90 and 120.
30
Common
Factors
Once
90
3
120
4
Remaining
Factors
LCM  30  3  4
LCM  360
Using Upside-Down Division to Find the LCM
3
Common
Factors
Once
18x y
3
18
6
2
3
12xy
12
4
2
2
Remember to take every variable
to the highest power
LCM  3  2  3  2  x  y
3 2
LCM  36x y
3
2