1. More on Multiplication and Multiples What do playing cards have to do with Multiplication?

2. They are a fun way to practice Multiplication problems Rules: all face cards are 12, red are negative, black are positive You will have just 3 seconds to write the answer down for each multiplication problem, Good Luck

3. Here are the answers, check your answers – how many out of 8 did you get right? -24 -72 27 -32 -60 10 -40 -24 By knowing the multiplication table, it makes finding multiples much easier.

4. We are now going to look at common multiples or a multiple that 2 numbers share. Take 4 & 7 Count by 4’s or add a 4 each time Count by 7’s or add a 7 each time What multiple do they share? When they are written down like this it’s easy to see that they share 28. So then 28 is called a common multiple. Notice that it is also the smallest common multiple in both lists, because it is we call 28 the Least Common Multiple or LCM The common multiple also has a third name. If both 4 and 7 are on the bottom of a fraction, the multiple is called the Common Denominator.

5. Find a common multiple for the numbers 4 and 6. Start at 4 and count by 4’s or add a 4 each time Start at 6 and count by 6’s or add a 6 each time What multiples do they share? They share 12, 24, 36, 48, 60 and on and on and on What is the Least Common Multiple or LCM (it is 12, smallest on the list) What would be a Common Denominator for 4 and 6 (any of the multiples could be) Watch for any pattern to finding common multiples?

6. Student Practice #1 Find the LCM or Least Common Multiple for 6 and 8. Start at 6 and count by 6’s or add a 6 each time Start at 8 and count by 8’s or add a 8 each time What multiples do they share? They share 24, 48, 72 and on and on and on What is the Least Common Multiple or LCM (it is 24, smallest on the list) What would be a Common Denominator for 6 and 8 (24 or 48, or 72…)

7. Student Practice #2 Find the LCM or Least Common Multiple for 7 and 12. Start at 7 and count by 7’s or add a 7 each time, continue at least 12 times, why? Start at 12 and count by 12’s or add a 12 each time What multiples do they share? They share 84, all multiples of 84 will now be common multiples, why? What is the Least Common Multiple or LCM (it is 84 smallest on the list) What would be a Common Denominator for 6 and 8 (84, 168 …)

8. Student Practice #3 Find the LCM for 4, 6, and 9 and 2 other common multiples Start at 4 and count by 4’s or add a 4 each time, continue at least 9 times, why? Start at 6 and count by 6’s or add a 6 each time To find two more common multiples, find multiples of the LCM 36 or 72 (2x36), and 108 (3x36) What is the Least Common Multiple or LCM (36) What would be a Common Denominator for 4, 6, and 9 (36, or 72 or 108) Start at 9 and count by 9’s or add a 9 each time

9. Student Practice #4 Find a common denominator for 8 and 10 Start at 8 and count by 8’s or add a 8 each time, continue at least 10 times, why? Start at 10 and count by 10’s or add a 10 each time A common denominator is 40 or 80 The Least Common Multiple or LCM is (40)