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

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.

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

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, – 24, 48, 72, 96, 120

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

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.

Method Numbers in common are 2 and 3 Leftover numbers are 2 and 3 2 x 3 x 2 x 3 = 36

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

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

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

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.)

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?