Transcript LCM & GCF

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)
d) State the answer
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
d) State the answer
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