2. Factors & Multiples Copyright©2001 Lynda Greene Finding multiples & LCM (least common multiple)

3. Introduction to Multiples What are they and how do I find them?

4. How to find Multiples: Multiply each number by 1, 2, 3, etc.., the ANSWERS (in red) are called multiples. Multiples of 2: 2x1= 2 2x2= 4 2x3= 6 2x4= 8 2x5= 10 etc. The ANSWERS (2,4,6,8,10,...) are the multiples of two

5. Practice Problems: (Hit enter to see the answers) Find the first five multiples for each of the following numbers 1) 5 5) 15 2) 7 6) 2 3) 12 7) 9 4) 3 8) 4 Answers: 1) 5, 10, 15, 20, 25 2) 7, 14, 21, 28, 35 3) 12, 24, 36, 48, 60 4) 3, 6, 9, 12, 15 5) 15, 30, 45, 60, 75 6) 2, 4, 6, 8, 10 7) 9, 18, 27, 36, 45 8) 4, 8, 12, 16, 20

6. Least Common Multiple (LCM)

7. THE LEAST COMMON MULTIPLE (LCM) Just like we learned with the GCF, the name LCM tells you what to do and what to look for. We want: Least: The smallest number Common: all the terms have in common Multiple: from a list of their multiples In other words: 1) Find all the multiples 2) Pick the smallest multiple they all have in common (this is the LCM) LCM of 2 and 3 is 6 Multiples of 3: 3x1= 3 3x2= 6 3x3= 9 3x4= 12 3x5= 15 Multiples of 2: 2x1= 2 2x2= 4 2x3= 6 2x4= 8 2x5= 10 Example: Find the LCM of 2 and 3

8. EXAMPLE: Find the LCM for the numbers 3, 4 and 6. 3 4 6 The multiples of each number 3, 6, 9, 12, 15, 18,... 4, 8, 12, 16, 20, 24,... 12 is the smallest number all three lists have in common. LCM = 12 6, 12, 18, 24, 30,...

9. Practice Problems: (I, WE, YOU) Find the LCM for the following numbers 1) 3, 5 2) 2, 4, 6 3) 21, 6 4) 4, 12 5) 20, 25 6) 4, 6 7) 13, 3 8) 4, 5, 20 Answers: 1) 15 2) 12 3) 42 4) 12 5) 100 6) 12 7) 39 8) 20

10. Practice Problems: (Sage and Scribe) Shoulder Partner – Shortest Person is Sage first Find the LCM for the following numbers 1) 6, 8 2) 14, 8 3) 21, 6, 7 4) 15, 5, 9 Answers: 1) 24 2) 56 3) 42 4) 45