1. Least Common Multiple A multiple of a number is the product of the number and a nonzero whole number.

2. The first five non-zero multiples of 5 are: 5, 10, 15, 20, 25. The first five non-zero multiples of 2 are: 2, 4, 6, 8, 10. We have seen that numbers can have common factors. They also have common multiples.

3. There are two methods for finding LCM. 1. M ake a list 2. U se prime factorization

4. METHOD 1 Make A List List the first few multiples of each number. The smallest number on both (all) lists is the LCM. 12 – 12, 24, 36, 48, 60 24 – 24, 48, 72, 96, 120

5. List the multiples of 4: List the multiples of 6: Common multiples of 4 and 6 include 12 and 24. The LCM is ____________.

6. METHOD 2 -Prime factorizatio n 1)Complete the prime factorization for both numbers. 2)Write down the number(s) they have in common only once. 3)Write down the leftover numbers. 4)Multiply them all together.

7. Method 2 18 2 3 3 12 3 4 22 9 Numbers in common are 2 and 3 Leftover numbers are 2 and 3 2 x 3 x 2 x 3 = 36

8. 35 57 420 10 42 2 5 67 3 2 245 549 77 Numbers they have in common: 5 and 7 Leftover numbers: 2, 3, 2, 7 Multiply them all together: 5 x 7 x 2 x 3 x 2 x 7 = 2940

9. Study Tip!!!!! Don’t list too many multiples of one number before beginning the other list. You may write many more than you need

10. 8: 8, 16, 24, 32, 40, 48, 56 10: 10, 20, 30, 40, 50 Find the LCM of 8 and 10. LCM = __________________

11. In one part of a musical composition, the triangle player in an orchestra plays once every 12 beats. The tympani player plays once every 9 beats. How often do they play together? (Hint: You need to find the LCM of 12 and 9.)

12. A Problem for You A local restaurant is offering a free meal to every 25 th customer on Valentine’s Day and a bouquet of roses to every 12 th customer. Which customer will be the first to get both a free meal and a free bouquet?