Title: Greatest Common Factor and Least Common Multiples GCF and LCM
1Greatest Common Factor and Least Common
MultiplesGCF and LCM
2What is the difference between a factor and a
multiple?
3Give me an example of a factor of 15
4Give me an example of a multiple of 15
5How would you find the GCF of 60 and 96?
6There are actually 3 ways. You can use prime
factorization, write out all the prime factors
for each number or extract common prime numbers.
7List 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
8or 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
9or you can extract the common prime factors of
60 and 96 and form a product to give the GCF.
This, to me, is the easiest way. Try it!
60, 96
2
2 x 2 x 3 12
2
30, 48
15, 24
3
5, 8
10Find the GCF (HCF) of 36, 24, 144 and 96
1196
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
1236, 24, 144, 96
2
2 x 2 x 3 12
18, 12, 72, 48
2
9, 6, 36, 24
3
3
2
12
8
13There are 3 ways to find the LCM as well. You
can list the multiples of the numbers, do prime
factorization, or extract the prime factors from
either one or both numbers.Find the LCM of 12
and 18
14Multiples 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.
15or 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
16Rememberthe numbers you pull out have to be
prime numbers!
12, 18
2
6, 9
2
3
3, 9
1, 3
3
1
1
2 x 2 x 3 x 3 36
17Find the LCM of 35, 420 and 245
18245
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
19primes
35, 420, 245
5
7, 84, 49
7
1, 12, 7
7
3
1, 12, 1
1, 4, 1
2
1, 2, 1
2
1, 1, 1
5 x 7 x 7 x 3 x 2 x 2 2940
20Find the GCF and LCM of 28 and 63
217 28 63 4 9
GCF 7
LCM 7 x 4 x 9 252
22Find the GCF and LCM of12 and 13
231 12 13
GCF 1
LCM 1 x 12 x 13 156
24Find the GCF and LCM of 27, 21, 33 and 15
253 27 21 33 15 9 7 11 5
GCF 3
LCM 3 x 9 x 7 x 11 x 5 10,395
26Start tonights homework. No calculators!