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**Least Common Multiple LCM**

4-6 6th grade math Least Common Multiple LCM

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Objective To find the least common multiple (LCM) of two or three numbers. Why? To help you find the common denominator when simplifying fractions. To help you find a commonality between numbers.

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**California State Standards**

NS 2.4 : Determine the least multiple … of whole numbers … MR 3.3: Develop generalizations of the results obtained and the strategies used and apply them in new problem situations.

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**Vocabulary Least Common Multiple (LCM) Multiples**

The least number, other than zero, that is a multiple of each of two or more numbers 4 = 12 3 = 12 Multiples The product of a given number and another whole number 2 = 2, 4, 6, 8 ,10, … ∞

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**How to Find the LCM Train A travels at 10 sec Train B travels at 6 sec**

When will both first pass each other? Use LCM. List the first 5 or so multiples of the larger number. Then start with the smaller multiple and ask: does this multiple share with this other number. If yes, that is you LCM. If not, move on and continue to ask the same question until you find the LCM. You will always have an LCM. 10 = 10, 20, 30, 40, 50 6 = LCM = 30 Trains will first pass each other in 30 sec.

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Another way to find LCM 84 = 72 = PF 84 = 2, 2, 3, 7 PF 72= 2, 2, 3, 2, 3 2 · 2 · 3 · 7 · 2 · 3 = LCM =504 84 2 42 21 3 7 Find the prime factorization of each number. Write each PF aligning common factors. Write the product in a list, using each common factor once and each other factor once. Multiply. (good strategy to use with larger numbers) 72 2 36 18 9 3

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**Try It! 5 = 6 = 6, 12, 18, 24, 30, LCM = 30 Find LCM 2) 3 = 5, 6**

7 = 7, 14, 21, 28, LCM = 21 3) 3 = 9 = 9, 18, 17, Find LCM 5, 6 3, 7 3, 9

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Try Some More! 4) PF 4 = 2, 2 PF 14 = 2, 7 LCM = 2 · 2 · 7 = 28 5) PF 4 = 2, 2 PF 6 = 2, 3 PF 8 = 2, 2, 2 LCM = 2 · 2 · 3 · 2 = 24 4 2 14 2 7 4) 4, 14 5) 4, 6, 8 8 2 4 4 2 6 2 3

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Objective Review To find the least common multiple (LCM) of two or three numbers. Why? You can now find the common denominator when simplifying fractions. You can now find a commonality between numbers.

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**Independent Practice Complete problems 7-12**

Copy original problem first. Show all work! If time, complete Mixed Review: 13-19 If still more time, work on Accelerated Math.

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