Least Common Multiples

Common Multiple

a common multiple is a multiple that two or more numbers share

Least common multiple

The smallest positive number that is a multiple of two or more numbers. Examples: To find the _________________________ of (12, 4) you can find the numbers multiples or find the numbers prime factors.

LCM(1,2,3)

6

Prime number

A whole number greater than 1 that has exactly two whole number factors, 1 and itself. Examples: 5 can only be divided evenly by 1 or 5, so it is a __________________. But 6 can be divided evenly by 1,2,3,and 6 and so 6 is not a prime number it is a composite number.

Prime factorization

Finding the factors of a number that are all prime Examples: To find the ______________________ of 45, use a factor tree to find that 45 is 5x9, and 9 is 3x3. So the __________________________ of 45 is 5x3x3.

Multiples

Numbers that can be divided into a given number evenly. These numbers will all be greater than the given number. Example: The _________ of 6 are 6, 12, 18, 24, 30 and so on. The number 6 can be divided evenly into the numbers 6, 12, 18, 24, 30 and so on

Factors

Numbers that when multiplied together give you the given number. These numbers will all be equal to or less than the given number. Example: The ___________ of 12 are 1,2,3,4,6,12. 2x6=12. 1x12=12. 3x4=12

Greatest Common Factor (GCF)

The greatest number that is a factor of two or more given numbers.

lcm(12,9)

36

30,18

(Least Common Mulitiple) 90

16,48

(Least Common Mulitple) 48

7,15

(Least Common Multiple) 105

40,15

(Least Common Multiple) 120

15,50

(Least Common Multiple) 150

9,6

(Least Common Multiple) 18

10,36

(Least Common Multiple) 180

24,64

(Least Common Multiple) 192

20,5

(Least Common Multiple) 20

8,12

(Least Common Multiple) 24

5,6

(Least Common Multiple) 30

9,12

(Least Common Multiple) 36

20,8

(Least Common Multiple) 40

4,15

(Least Common Multiple) 60

28,42

(Least Common Multiple) 84

7,12

(Least Common Multiple) 84

18,10

(Least Common Multiple) 90

16,96

(Least Common Multiple) 96

LCM(1,2,3,4)

12

lcm(90, 342)

1710