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```LCM & GCF
GCF
• Means Greatest Common Factor
Or Largest Common Factor
Find the GCF of 28 and 42
•
There are at least three ways to do this:
a) Make a list of all factors for both numbers
b) Create an area model
c) Use prime factorization
Make a list of all factors for both numbers (28, 42)
a) Create all multiplication sentences that have a product of
28:
{1 x 28, 2 x 14, 4 x 7, 7 x 4, 14 x 2, 28 x 1}
b) Create all multiplication sentences that have a product of
42:
{1 x 42, 2 x 21, 3 x 14, 6 x 7, 7 x 6, 14 x 3, 21 x 2, 42 x 1}
c) Make a list of common factors:
{1, 2, 4, 7, 14}
d) Choose the largest (greatest) common factor (14)
e) State the answer: “The GCF of 28 and 42 is 14”
Create an area model (each square = 2 cm2
42
28
a) Use the two numbers that you want to
find the GCF for.
b) Build a rectangle with those dimensions
c) Find the largest square that will tile the
rectangle (no gaps or overlaps)
Prime Factorization
a)
Create the prime factorization for each number:
28
42
2 x 14
2 x 21
2x2x7
2x3x7
b) Circle pairs of common factors:
2x2x7
2x3x7
c) Create a multiplication sentence using ONLY common
factors: 2 x 7 = 14
d) Write the answer: the GCF of 28 and 42 is 14
LCM
• Means Least Common Multiple
or First (smallest) common multiple
Find the LCM of 39 and 52
There are at least two ways to do this:
a) Make a list of multiples of each number
b) Use prime factorization
Make a list
( LCM: 39,52)
a)
Make a list of multiples:
{ 39, 78, 117, 156, 195, 234, 273, 312, 351, 390,
429, 468, 507, 546, 585, 624, …}
{52, 104, 156, 208, 260, 312, 364, 416, 468, 520,
572, 624, 676, …}
b) Look for common multiples:
{156, 312, 468, 624, …}
c) Find the smallest (least common multiple): 156
Use prime Factorization
a)
Find the prime factors:
39= 3 x 13
52 = 2 x 2 x 13
b) Circle pairs of common factors:
3 x 13
2 x 2 x 13
c) Write a multiplication sentence that contains every unique prime factor
and one of each common prime factor.
or use all the factors, leave out the doubles:
2 x 2 x 3 x 13 = 156
d) The LCM of 39 and 52 is 156
39
3
52
2
2
LCM
2
2
13
13
3
13
```