Lesson 4-5 LCM: Least Common Multiple

Multiples A multiple is formed by multiplying a given number by the counting numbers. The counting numbers are 1, 2, 3, 4, 5, 6, etc. DON’T GET THEM CONFUSED WITH FACTORS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Factors are few but multiples are many.

Example: List the multiples of 4: 4 x 1 = 4 4 x 2 = 8 4 x 3 = 12 4 x 4 = 16 4 x 5 = 20 4 x 6 = 24 Counting Numbers So, the multiples of 4 are 4, 8, 12, 16, 20, 24, 28, etc.

What are the first five multiples of 13? 13 x 1 =13 13 x 2 = x 3 = x 4 = x 5 = 65 13, 26, 39, 52, 65

Find the Missing Multiples 6, 12, 18, ____, ____ ___, 6, 9, 12, ____, ____, 21 ___, 24, 36, 48, 60, ____

Least Common Multiple (LCM) The least common multiple is the smallest number that is common between two lists of multiples.

Method #1: Find the LCM of the numbers by listing the multiples till you find a match The multiples of 12: 12 x 1 = x 2 =24 12 x 3 = x 4 = x 5 =60 The multiples of 18: 18 x 1 = x 2 = x 3 = x 4 = x 5 = 90

12, 24, 36, 48, 60 18, 36, 54, 72, 90 The first number you see in both lists is 36. The least common multiple of 12 and 18 is 36.

Example 2: Find the LCM of 9 and 10 9, 18, 27, 36, 45, 54, 63, 72 10, 20, 30, 40, 50, 60, 70, 80 If you don’t see a common multiple, make each list go further. 81, 90, 99 90, 100, 110 The LCM of 9 and 10 is 90

Method #2: Use Prime Factorization 1. Find the prime factorization of each number 2. Find the common factors 3. Multiply all the common factors PLUS the remaining factors together. Example: Find the LCM of 18 and = 2 x 3 x 3 30 = 2 x 3 x 5 LCM = 2 x 3 x 3 x 5 = 90

Now Let’s review GCF!