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## Least Common Multiples (LCM)

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**Definition**Smallest number that is a multiple of 2 or more numbers.**Find the LCM of 6 and 10**STEP 1: Find the smallest prime number that goes into all of the given numbers. Continue until you have at least one prime number. 2 6 10 3 5 STEP 2: Multiply all of the numbers on the side and on the bottom row. 2 ∙ 3 ∙ 5 = 30 LCM = 30**Find the LCM of 6 and 12**2 6 12 3 6 3 1 2 2 ∙ 3 ∙ 1 ∙ 2 = 12 LCM = 12**No Common Factors - Primes**If the numbers have no common factors, simply multiply them together. 15 4 3 7 15 ∙ 4 = 60 3 ∙ 7 = 21 LCM = 21 LCM = 60**Find the LCM of 9 and 12**3 9 12 3 4 3 ∙ 3 ∙ 4 = 36 YOUR TURN LCM = 36**Find the LCM of 7 and 10**7 10 7 ∙ 10 = 70 LCM = 70 YOUR TURN**Find the LCM of 20 and 30**2 20 30 10 15 5 2 3 2 ∙ 5 ∙ 2 ∙ 3 = 60 YOUR TURN LCM = 60**Find the LCM of 8 and 12**Step 1: List the multiples of each number Step 2: Circle the smallest number that is in all the lists. Step 3: Write the answer 8, 16, 24, 32 12, 24 LCM = 24**Find the LCM of 6, and 9**6, 12, 18 9, 18 YOUR TURN**Using Multiples to Find the LCM**Find the least common multiple (LCM). Method 2: Use a list. 4, 5, and 8 4: 4, 8, 12 , 16, 20, 24, 28, 32, 36, 40, 44, . . . List multiples of 4, 5, and 8. 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, . . . Find the smallest number that is in all the lists. 8: 8, 16, 24, 32, 40, 48, . . . LCM: 40**Problem Solve: Consumer Application**English muffins come in packs of 8, and eggs come in cartons of 12. If there are 24 students, what is the least number of packs and cartons needed so that each student has a muffin sandwich with one egg and there are no muffins left over? There are 24 English muffins and 24 eggs. So 3 packs of English muffins and 2 cartons of eggs are needed.**2**8 12 4 6 2 2 3**John has a baseball game every 6 days and a football game**every 9 days. John is playing both a baseball and a football game today. How many days is it until John plays both a baseball and a football game on the same day again? 18 days**Fatima is buying hot dogs for a class picnic. Hot dogs are**sold in packages of 10. Hot dogs buns are sold in packages of 8. What is the smallest number of hot dogs and buns Fatima can buy to have an equal number of each? 40 hot dogs & buns, 4 packs of hot dogs, and 5 packs of buns