Notes 3.1 Least Common Multiples

A multiple of a number is the product of the number and any whole number greater than zero.

Of all the multiples of two numbers, thesmallest is called the least commonmultiple.

Finding least common multiple (lcm):1. List the prime factorization of the first number.2. List the prime factorization of the second number.3. Circle any factors they have in common.4. List the factors of both, writing any circled factors only once.5. Multiply the factors in the list to get the least common multiple.

Example: 24 = 2 * 2 * 2 * 3 30 = 2 * 3 * 5 lcm = 2 * 2 * 2 * 3 * 5 lcm = 120

A second method to find lcm:1. List the multiples of each number.2. Stop when you have a match.

Example: 24 = 24, 48, 72, 96, 120, 144, … 30 = 30, 60, 90, 120, … lcm = 120

URL of the dayURL of the day

http://www.helpwithfractions.com/lehttp://www.helpwithfractions.com/least-common-multiple.htmlast-common-multiple.html

Homework answersHomework answers7) 2, 4, 6, 8, 10, 12, 14, 16;7) 2, 4, 6, 8, 10, 12, 14, 16;

7, 14, 21, 28, 35, 42, 49, 56; 7, 14, 21, 28, 35, 42, 49, 56;

1414

8)8) 6, 12, 18, 24, 30, 36, 42, 48;6, 12, 18, 24, 30, 36, 42, 48;

9, 18, 27, 36, 45, 54, 63, 72;9, 18, 27, 36, 45, 54, 63, 72;

1818

9)9) 4, 8, 12, 16, 20, 24, 28, 32;4, 8, 12, 16, 20, 24, 28, 32;

20, 40, 60, 80, 100, 120, 140, 160;20, 40, 60, 80, 100, 120, 140, 160;

2020

10)10) 12, 24, 36, 48, 60, 72, 84, 96;12, 24, 36, 48, 60, 72, 84, 96;

14, 28, 42, 56, 70, 84, 98, 112;14, 28, 42, 56, 70, 84, 98, 112;

8484

11)11) 4, 8, 12, 16, 20, 24, 28, 32;4, 8, 12, 16, 20, 24, 28, 32;

6, 12, 18, 24, 30, 36, 42, 48;6, 12, 18, 24, 30, 36, 42, 48;

8, 16, 24, 32, 40, 48, 56, 64; 8, 16, 24, 32, 40, 48, 56, 64;

2424

12)12) 2x2x7; 2x2x2x2x2: 22x2x7; 2x2x2x2x2: 255x7=224x7=224

13)13) 2x23; 5x23: 2x5x25=2302x23; 5x23: 2x5x25=230

14)14) 5x7; 2x2x2x5: 25x7; 2x2x2x5: 233x5x7=280x5x7=280

15)15) 2266; 2; 233x3x322: 2: 266x3x322=576=576

16)16) 2; 3; 5: 2x3x5=302; 3; 5: 2x3x5=30

18)18) 4, 6; 12 4, 6; 12 19)19) 6, 9; 18 6, 9; 18

20)20) 10, 15; 30 10, 15; 30 21)21) 2x3xn 2x3xn

24)24) B B 25)25) C C

26)26) mpa; Find the lcm of 15 and 25, mpa; Find the lcm of 15 and 25, which is 75. Then divide 1000 by 75 which is 75. Then divide 1000 by 75 to get 33 1/3. So, they will give to get 33 1/3. So, they will give away 13 t-shirts for each 1000 away 13 t-shirts for each 1000 packages.packages.