Download Greatest Common Factor and Least Common

Greatest Common Factor and
Least Common Multiples
GCF 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 60:
1,2,3,4,5,6,10,12,15,20,30,60
List the factors of 96
1,2,3,4,6,8,12,16,24,32,48,96
find 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
15
2
24
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
18
2
12
24
2
9
2
6
2
12
2
3
2
3
3
144
2
12
12
3
3
4
2 x 2 x 3 = 12
4
2
2
6
2
2
2
3
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 are…
12,24,36,48,60,72,….
Multiples of 18 are…
18,36,54,72,90,108,…
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
4
3
2
9
2
2
3
3
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
35
42
10
5
245
420
5
49
7
2
5
6
3
7
7
2
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
7