1. 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, the smallest is called the least common multiple.

2. 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.

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

4. 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

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6. Homework answers 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; 14 14 8) 6, 12, 18, 24, 30, 36, 42, 48; 9, 18, 27, 36, 45, 54, 63, 72; 9, 18, 27, 36, 45, 54, 63, 72; 18 18 9) 4, 8, 12, 16, 20, 24, 28, 32; 20, 40, 60, 80, 100, 120, 140, 160; 20, 40, 60, 80, 100, 120, 140, 160; 20 20

7. 10) 12, 24, 36, 48, 60, 72, 84, 96; 14, 28, 42, 56, 70, 84, 98, 112; 14, 28, 42, 56, 70, 84, 98, 112; 84 84 11) 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; 24 24 12) 2x2x7; 2x2x2x2x2: 2 5 x7=224 13) 2x23; 5x23: 2x5x25=230 14) 5x7; 2x2x2x5: 2 3 x5x7=280

8. 15) 2 6 ; 2 3 x3 2 : 2 6 x3 2 =576 16) 2; 3; 5: 2x3x5=30 18) 4, 6; 12 19) 6, 9; 18 20) 10, 15; 30 21) 2x3xn 24) B 25) C 26) mpa; Find the lcm of 15 and 25, which is 75. Then divide 1000 by 75 to get 33 1/3. So, they will give away 13 t-shirts for each 1000 packages.