Lesson 3-3
Objective - To find the Least Common Multiple
(LCM) of two whole numbers.
GCF vs. LCM
GCF = 4
LCM - Least Common Multiple - Smallest
number that a set of given numbers divides
evenly into.
16
GCF - Reduce or Simplify
16 ÷4 = 4
20 ÷4 5
20
LCM = 80
LCM - Compare, Add, or Subtract
Two ways to find the LCM
1) Make a list of multiples.
( 55 ) 165
2) Use the prime factorizations to select
the common factors once plus all the
remaining factors.
Make a list of the multiples less than 50 and
circle the common multiples.
1) 6, 8
25
80
()
7 4
20 4
28
80
Make a list of the first eight multiples and
circle the LCM.
1) 3, 7
6: 6, 12, 18, 24, 30, 36, 42, 48
3: 3, 6 , 9 , 12, 15, 18, 21, 24
8: 8, 16, 24, 32, 40, 48
7: 7, 14, 21, 28, 35, 42, 49, 56
2) 2, 4,16
2) 4, 12
2: 2, 4 , 6 , 8 , 10, 12, 14, 16
4: 4, 8 , 12, 16, 20, 24, 28, 32, 36, 40, 44, 48
12: 12 , 24 , 36 , 48
16: 16, 32, 48, 64 , 80 , 96, 112 , 128
Use prime factorization to find the LCM.
21
18
2
3
9
3
7
Use prime factorization to find the LCM.
45
48
5
9
3
3
2•3•3
4: 4, 8 , 12, 16, 20, 24, 28, 32
3• 7
Select all common factors once.
Then select the remaining factors.
LCM = 3 •2 •3 •7
LCM = 126
8
3
6
2 4 2 3
2 2
3• 3•5
2•2•2•2•3
Select all common factors once.
Then select the remaining factors.
LCM = 3 •3 •5 •2 •2 •2 •2
LCM = 720
Math 6 Slide Show: Teaching Made Easy As Pi, by Mike Mills and James Wenk © 2011
Lesson 3-3 (cont.)
Use prime factorization to find the LCM.
16
20
30
2
2 10
8
4
2
2
15
2
5
3 5
2•2•5
2•3•5
2
Use prime factorization to find the LCM.
18
30
40
2
2 15
9
3
3
3
20
2
5
2 10
2
2
2•2•2•2
Select all common factors once.
(common to all three or just two)
Then select the remaining factors.
LCM = 2 •2 •5 •2 •2 •3
LCM = 240
2•3•3
2 •3•5
5
2•2•2•5
Select all common factors once.
(common to all three or just two)
Then select the remaining factors.
LCM = 2 •3•5 •3 •2 •2
LCM = 360
Math 6 Slide Show: Teaching Made Easy As Pi, by Mike Mills and James Wenk © 2011