Least Common Factors and Greatest Common Factors

Greatest Common Factors and Least Common Multiples

Greatest Common Factor

When you find all the factors of two or more numbers, and you find some factors that sre the same ("common"), the largest of those common factors is the GREATEST COMMON FACTOR (GCF).

There are 2 ways to find the GCF:

• List all the factors of each number; the largest common factor is the GCF

• Find the prime factors of each number. The PRODUCT of the COMMON PRIME FACTORS is the GCF

Find the GCF of 8 and 12

List the factors of 8: 1, 2, 4, 8

List the factors of 12: 1, 2, 3, 4, 6, 12

List the common factors: 1, 2, 4

What is the GCF? 4

Least Common Multiples

A MULTIPLE of a number is the product of the number multiplied by a whole number. (6x1), (6x2), (6x3,) (6x4), (6x5), (6x6), (6x7), (6x8)....

(SKIP COUNTING)

A number has ENDLESS multiples. The multiples of 6 are:

6, 12, 18, 24, 30, 36, 42, 48......... (The list NEVER ENDS)

Least Common Multiples (LCM)

• Common multiples are multiples that are shared by two or more numbers

• The LCM is the smallest multiple that is shared by two or more numbers.

There are 2 ways to find the LCM

• List several multiples of each number until you find one that the numbers have in common

• Find the prime factors of each number; have a contest to see which number has the most of each prime factor; MULTIPLY the prime factors from the "Contest".

Find the LCM of 2 and 3

List the multiples of 2:

2, 4, 6, 8, 10, 12, 14, 16, 18......... (Never ends)

List the multiples of 3:

3, 6, 9, 12, 15, 18, 21, 24..........(Never ends)

Common multiples: 6, 12, 18,

LCM: 6

Open Ended

List the first 6 multiples of 8:

(The first multiple is 8x1)

Open Ended

Is it possible to list ALL of the multiples of 12? Explain.

Open Ended

What is the difference between a multiple and a factor?