Exercise
State whether 51 is prime
or composite.
composite
Exercise
State whether 97 is prime
or composite.
prime
Exercise
Write the prime
2
2
•
3
•5
factorization of 90.
Exercise
Write the prime
factorization of 150. 2 • 3 • 52
Exercise
Find the greatest common
factor of 90 and 150.
2 • 3 • 5 = 30
1x 2x 3x 4x
multiples of 3
multiples of 4
3
4
6
8
9 12
12 16
5x 6x 7x 8x
multiples of 3 15 18 21 24
multiples of 4 20 24 28 32
Least Common Multiple
The least common multiple
of two or more numbers is
the smallest number that is
a multiple of each of the
given numbers.
Example 1
List multiples to find the
LCM of 10 and 12.
10: 10, 20, 30, 40, 50, 60, 70…
12: 12, 24, 36, 48, 60, 72, 84…
The LCM of 10 and 12 is 60.
Using Listing to Find the
Least Common Multiple
1. List the multiples of each
number.
2. Identify the first common
multiple in each list of
multiples.
Example
List multiples to find the
LCM of 8 and 6. 24
Example
List multiples to find the
LCM of 15 and 36. 180
Using Exponential Form to
Find the LCM
1. Write the prime
factorization of each
number in exponential
form.
Using Exponential Form to
Find the LCM
2. Identify all the prime
factors, both the common
and different prime
factors, that appear in the
factorizations.
Using Exponential Form to
Find the LCM
3. Find the product of all the
prime factors, using only
the highest power of each
that appears in any of the
factorizations.
Example 2
Find the LCM of 30 and 45.
30: 2 • 3 • 5
45: 3 • 3 • 5 = 32 • 5
LCM = 2 • 32 • 5 = 90
Example 3
Find the LCM of 12, 28, and
75.
12: 2 • 2 • 3 = 22 • 3
28: 2 • 2 • 7 = 22 • 7
75: 3 • 5 • 5 = 3 • 52
LCM = 22 • 3 • 52 • 7
= 4 • 3 • 25 • 7 = 2,100
Example
Use prime factorizations to
find the LCM of 40 and 50.
200
Example
Use prime factorizations to
find the LCM of 21 and 49.
147
Example
Use prime factorizations to
find the LCM of 32, 18,
and 72.
288
Example
Use prime factorizations to
find the LCM of 42, 45,
and 63.
630
LCM of 4x and
2
4x
2
3ab
2
5a b
3y
4z
Example 4
Find the LCM of 15x3y
and 21x2.
15x3y: 3 • 5 • x • x • x • y
21x2: 3 • 7 • x • x
3 • 5 • 7 = 105 x3 and y
LCM = 105x3y
Example
Find the LCM of 12ab
and 15b2c. 60ab2c
Example
Find the LCM of 63x2y3
and 72x3y4. 504x3y4
Example
Find the LCM of 8mn2, 36m3n
and 9m.
72m3n2
Example
Find the LCM of 84r, 21s
and 14t.
84rst
Exercise
Find the GCF and LCM of 36
and 48. GCF: 12; LCM: 144
Exercise
Find the GCF and LCM of 12,
18, and 24. GCF: 6; LCM: 72
Exercise
For any two numbers, what
would be the least common
factor? 1
Exercise
For any two numbers, what
would be the greatest
common multiple?
Exercise
When you reduce fractions
350
such as
, are you using
400
an LCM or a GCF? How?
Exercise
When you add fractions
1
1
7
such as 6 and 8 to get 24 ,
are you using an LCM or a
GCF? How?