Slide 1

the largest number that can divide
into all of the numbers.
Find the GCF of 42 and 60.
Write the prime factorization of
each number.

42 2
21 3
7 7
1

60
30
15
5

2
2
3
5

1
What prime factors do the numbers have in common?
Multiply those numbers with the lowest exponents .
The GCF is 2 x 3 = 6
6 is the largest number that can go into 42 and 60!

 Find the GCF of

 12 and

18
 18 and 27
 24 and 30
 36 and 45
 24 and 36
 16, 32 and 40
 18,27 and 36

Find the HCF of :
1)
2)
3)
4)
5)

2x3x5 and 2x3x7
2x3x5x7 and 2x2x3x11
2x2x3x5 and 2x2x3x11
2x2x2x5x7 and 2x2x2x5x11
2x2x2x7x7 and 2x2x2x7x11

 the smallest number that is common

between two lists of multiples.

42 2
21 3
7 7
1

60
30
15
5

2
2
3
5

1
Write the common and non common factors
with the greatest exponents
The LCM of 42 and 60 is 420.

Find the LCM of the following

1.30 and 25
2. 32 and 8
3. 12, 32 and 4
4. 3 and 9
5. 2,4 and 6

1. 2x5 and 5x5
2. 2x2x3 and 2x2x5
 3. 2x2x3 and 2x7
4.2x2x2 and 2x7
5. 2x2x5 and 5x5


Slide 2

the largest number that can divide
into all of the numbers.
Find the GCF of 42 and 60.
Write the prime factorization of
each number.

42 2
21 3
7 7
1

60
30
15
5

2
2
3
5

1
What prime factors do the numbers have in common?
Multiply those numbers with the lowest exponents .
The GCF is 2 x 3 = 6
6 is the largest number that can go into 42 and 60!

 Find the GCF of

 12 and

18
 18 and 27
 24 and 30
 36 and 45
 24 and 36
 16, 32 and 40
 18,27 and 36

Find the HCF of :
1)
2)
3)
4)
5)

2x3x5 and 2x3x7
2x3x5x7 and 2x2x3x11
2x2x3x5 and 2x2x3x11
2x2x2x5x7 and 2x2x2x5x11
2x2x2x7x7 and 2x2x2x7x11

 the smallest number that is common

between two lists of multiples.

42 2
21 3
7 7
1

60
30
15
5

2
2
3
5

1
Write the common and non common factors
with the greatest exponents
The LCM of 42 and 60 is 420.

Find the LCM of the following

1.30 and 25
2. 32 and 8
3. 12, 32 and 4
4. 3 and 9
5. 2,4 and 6

1. 2x5 and 5x5
2. 2x2x3 and 2x2x5
 3. 2x2x3 and 2x7
4.2x2x2 and 2x7
5. 2x2x5 and 5x5


Slide 3

the largest number that can divide
into all of the numbers.
Find the GCF of 42 and 60.
Write the prime factorization of
each number.

42 2
21 3
7 7
1

60
30
15
5

2
2
3
5

1
What prime factors do the numbers have in common?
Multiply those numbers with the lowest exponents .
The GCF is 2 x 3 = 6
6 is the largest number that can go into 42 and 60!

 Find the GCF of

 12 and

18
 18 and 27
 24 and 30
 36 and 45
 24 and 36
 16, 32 and 40
 18,27 and 36

Find the HCF of :
1)
2)
3)
4)
5)

2x3x5 and 2x3x7
2x3x5x7 and 2x2x3x11
2x2x3x5 and 2x2x3x11
2x2x2x5x7 and 2x2x2x5x11
2x2x2x7x7 and 2x2x2x7x11

 the smallest number that is common

between two lists of multiples.

42 2
21 3
7 7
1

60
30
15
5

2
2
3
5

1
Write the common and non common factors
with the greatest exponents
The LCM of 42 and 60 is 420.

Find the LCM of the following

1.30 and 25
2. 32 and 8
3. 12, 32 and 4
4. 3 and 9
5. 2,4 and 6

1. 2x5 and 5x5
2. 2x2x3 and 2x2x5
 3. 2x2x3 and 2x7
4.2x2x2 and 2x7
5. 2x2x5 and 5x5


Slide 4

the largest number that can divide
into all of the numbers.
Find the GCF of 42 and 60.
Write the prime factorization of
each number.

42 2
21 3
7 7
1

60
30
15
5

2
2
3
5

1
What prime factors do the numbers have in common?
Multiply those numbers with the lowest exponents .
The GCF is 2 x 3 = 6
6 is the largest number that can go into 42 and 60!

 Find the GCF of

 12 and

18
 18 and 27
 24 and 30
 36 and 45
 24 and 36
 16, 32 and 40
 18,27 and 36

Find the HCF of :
1)
2)
3)
4)
5)

2x3x5 and 2x3x7
2x3x5x7 and 2x2x3x11
2x2x3x5 and 2x2x3x11
2x2x2x5x7 and 2x2x2x5x11
2x2x2x7x7 and 2x2x2x7x11

 the smallest number that is common

between two lists of multiples.

42 2
21 3
7 7
1

60
30
15
5

2
2
3
5

1
Write the common and non common factors
with the greatest exponents
The LCM of 42 and 60 is 420.

Find the LCM of the following

1.30 and 25
2. 32 and 8
3. 12, 32 and 4
4. 3 and 9
5. 2,4 and 6

1. 2x5 and 5x5
2. 2x2x3 and 2x2x5
 3. 2x2x3 and 2x7
4.2x2x2 and 2x7
5. 2x2x5 and 5x5


Slide 5

the largest number that can divide
into all of the numbers.
Find the GCF of 42 and 60.
Write the prime factorization of
each number.

42 2
21 3
7 7
1

60
30
15
5

2
2
3
5

1
What prime factors do the numbers have in common?
Multiply those numbers with the lowest exponents .
The GCF is 2 x 3 = 6
6 is the largest number that can go into 42 and 60!

 Find the GCF of

 12 and

18
 18 and 27
 24 and 30
 36 and 45
 24 and 36
 16, 32 and 40
 18,27 and 36

Find the HCF of :
1)
2)
3)
4)
5)

2x3x5 and 2x3x7
2x3x5x7 and 2x2x3x11
2x2x3x5 and 2x2x3x11
2x2x2x5x7 and 2x2x2x5x11
2x2x2x7x7 and 2x2x2x7x11

 the smallest number that is common

between two lists of multiples.

42 2
21 3
7 7
1

60
30
15
5

2
2
3
5

1
Write the common and non common factors
with the greatest exponents
The LCM of 42 and 60 is 420.

Find the LCM of the following

1.30 and 25
2. 32 and 8
3. 12, 32 and 4
4. 3 and 9
5. 2,4 and 6

1. 2x5 and 5x5
2. 2x2x3 and 2x2x5
 3. 2x2x3 and 2x7
4.2x2x2 and 2x7
5. 2x2x5 and 5x5


Slide 6

the largest number that can divide
into all of the numbers.
Find the GCF of 42 and 60.
Write the prime factorization of
each number.

42 2
21 3
7 7
1

60
30
15
5

2
2
3
5

1
What prime factors do the numbers have in common?
Multiply those numbers with the lowest exponents .
The GCF is 2 x 3 = 6
6 is the largest number that can go into 42 and 60!

 Find the GCF of

 12 and

18
 18 and 27
 24 and 30
 36 and 45
 24 and 36
 16, 32 and 40
 18,27 and 36

Find the HCF of :
1)
2)
3)
4)
5)

2x3x5 and 2x3x7
2x3x5x7 and 2x2x3x11
2x2x3x5 and 2x2x3x11
2x2x2x5x7 and 2x2x2x5x11
2x2x2x7x7 and 2x2x2x7x11

 the smallest number that is common

between two lists of multiples.

42 2
21 3
7 7
1

60
30
15
5

2
2
3
5

1
Write the common and non common factors
with the greatest exponents
The LCM of 42 and 60 is 420.

Find the LCM of the following

1.30 and 25
2. 32 and 8
3. 12, 32 and 4
4. 3 and 9
5. 2,4 and 6

1. 2x5 and 5x5
2. 2x2x3 and 2x2x5
 3. 2x2x3 and 2x7
4.2x2x2 and 2x7
5. 2x2x5 and 5x5


Slide 7

the largest number that can divide
into all of the numbers.
Find the GCF of 42 and 60.
Write the prime factorization of
each number.

42 2
21 3
7 7
1

60
30
15
5

2
2
3
5

1
What prime factors do the numbers have in common?
Multiply those numbers with the lowest exponents .
The GCF is 2 x 3 = 6
6 is the largest number that can go into 42 and 60!

 Find the GCF of

 12 and

18
 18 and 27
 24 and 30
 36 and 45
 24 and 36
 16, 32 and 40
 18,27 and 36

Find the HCF of :
1)
2)
3)
4)
5)

2x3x5 and 2x3x7
2x3x5x7 and 2x2x3x11
2x2x3x5 and 2x2x3x11
2x2x2x5x7 and 2x2x2x5x11
2x2x2x7x7 and 2x2x2x7x11

 the smallest number that is common

between two lists of multiples.

42 2
21 3
7 7
1

60
30
15
5

2
2
3
5

1
Write the common and non common factors
with the greatest exponents
The LCM of 42 and 60 is 420.

Find the LCM of the following

1.30 and 25
2. 32 and 8
3. 12, 32 and 4
4. 3 and 9
5. 2,4 and 6

1. 2x5 and 5x5
2. 2x2x3 and 2x2x5
 3. 2x2x3 and 2x7
4.2x2x2 and 2x7
5. 2x2x5 and 5x5


Slide 8

the largest number that can divide
into all of the numbers.
Find the GCF of 42 and 60.
Write the prime factorization of
each number.

42 2
21 3
7 7
1

60
30
15
5

2
2
3
5

1
What prime factors do the numbers have in common?
Multiply those numbers with the lowest exponents .
The GCF is 2 x 3 = 6
6 is the largest number that can go into 42 and 60!

 Find the GCF of

 12 and

18
 18 and 27
 24 and 30
 36 and 45
 24 and 36
 16, 32 and 40
 18,27 and 36

Find the HCF of :
1)
2)
3)
4)
5)

2x3x5 and 2x3x7
2x3x5x7 and 2x2x3x11
2x2x3x5 and 2x2x3x11
2x2x2x5x7 and 2x2x2x5x11
2x2x2x7x7 and 2x2x2x7x11

 the smallest number that is common

between two lists of multiples.

42 2
21 3
7 7
1

60
30
15
5

2
2
3
5

1
Write the common and non common factors
with the greatest exponents
The LCM of 42 and 60 is 420.

Find the LCM of the following

1.30 and 25
2. 32 and 8
3. 12, 32 and 4
4. 3 and 9
5. 2,4 and 6

1. 2x5 and 5x5
2. 2x2x3 and 2x2x5
 3. 2x2x3 and 2x7
4.2x2x2 and 2x7
5. 2x2x5 and 5x5


Slide 9

the largest number that can divide
into all of the numbers.
Find the GCF of 42 and 60.
Write the prime factorization of
each number.

42 2
21 3
7 7
1

60
30
15
5

2
2
3
5

1
What prime factors do the numbers have in common?
Multiply those numbers with the lowest exponents .
The GCF is 2 x 3 = 6
6 is the largest number that can go into 42 and 60!

 Find the GCF of

 12 and

18
 18 and 27
 24 and 30
 36 and 45
 24 and 36
 16, 32 and 40
 18,27 and 36

Find the HCF of :
1)
2)
3)
4)
5)

2x3x5 and 2x3x7
2x3x5x7 and 2x2x3x11
2x2x3x5 and 2x2x3x11
2x2x2x5x7 and 2x2x2x5x11
2x2x2x7x7 and 2x2x2x7x11

 the smallest number that is common

between two lists of multiples.

42 2
21 3
7 7
1

60
30
15
5

2
2
3
5

1
Write the common and non common factors
with the greatest exponents
The LCM of 42 and 60 is 420.

Find the LCM of the following

1.30 and 25
2. 32 and 8
3. 12, 32 and 4
4. 3 and 9
5. 2,4 and 6

1. 2x5 and 5x5
2. 2x2x3 and 2x2x5
 3. 2x2x3 and 2x7
4.2x2x2 and 2x7
5. 2x2x5 and 5x5


Slide 10

the largest number that can divide
into all of the numbers.
Find the GCF of 42 and 60.
Write the prime factorization of
each number.

42 2
21 3
7 7
1

60
30
15
5

2
2
3
5

1
What prime factors do the numbers have in common?
Multiply those numbers with the lowest exponents .
The GCF is 2 x 3 = 6
6 is the largest number that can go into 42 and 60!

 Find the GCF of

 12 and

18
 18 and 27
 24 and 30
 36 and 45
 24 and 36
 16, 32 and 40
 18,27 and 36

Find the HCF of :
1)
2)
3)
4)
5)

2x3x5 and 2x3x7
2x3x5x7 and 2x2x3x11
2x2x3x5 and 2x2x3x11
2x2x2x5x7 and 2x2x2x5x11
2x2x2x7x7 and 2x2x2x7x11

 the smallest number that is common

between two lists of multiples.

42 2
21 3
7 7
1

60
30
15
5

2
2
3
5

1
Write the common and non common factors
with the greatest exponents
The LCM of 42 and 60 is 420.

Find the LCM of the following

1.30 and 25
2. 32 and 8
3. 12, 32 and 4
4. 3 and 9
5. 2,4 and 6

1. 2x5 and 5x5
2. 2x2x3 and 2x2x5
 3. 2x2x3 and 2x7
4.2x2x2 and 2x7
5. 2x2x5 and 5x5