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Greatest Common Factor and Least Common

MultiplesGCF and LCM

What is the difference between a factor and a

multiple?

Give me an example of a factor of 15

Give me an example of a multiple of 15

How would you find the GCF of 60 and 96?

There are actually 2 ways. You can use prime

factorization, or write out all the prime

factors for each number.

List the factors of 601,2,3,4,5,6,10,12,15,20,3

0,60List the factors of 961,2,3,4,6,8,12,16,24

,32,48,96find the largest factor - 12

or do prime factorization. Circle all the

primes the 2 numbers have in common and multiply

one set of them to get your GCF.

96

60

48

2

2

30

24

2

15

2

12

2

3

5

6

2

2 x 2 x 3 12

2

3

Find the GCF (HCF) of 36, 24, 144 and 96

96

24

36

48

2

2

12

18

2

24

2

6

9

2

2

12

2

3

2

3

3

6

2

144

2

3

12

12

3

4

2 x 2 x 3 12

3

4

2

2

2

2

There are 2 ways to find the LCM as well. You

can list the multiples of the numbers or do prime

factorization. Find the LCM of 12 and 18

Multiples of 12 are12,24,36,48,60,72,.Multip

les of 18 are18,36,54,72,90,108,The

smallest multiple the 2 numbers have in common is

the least common multiple.

or do prime factorization. Write down the

number they have in common only once, then write

down the leftover numbers. Multiply them all

together.

12

18

9

4

2

3

3

3

2

2

Numbers in common are 2 and 3 Leftover numbers

are 2 and 3 2 x 3 x 2 x 3 36

Find the LCM of 35, 420 and 245

245

35

420

42

5

49

10

5

7

5

7

7

2

6

7

2

3

Numbers they have in common 5 and 7 Leftover

numbers 2, 3, 2, 7 Multiply them all together

5 x 7 x 2 x 3 x 2 x 7 2940

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