Arithmetic – Factorization Part 2 – LCM and GCD

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Multiple and Divisor/Factor

• Given two integers a, b, if a is divided by b, then a is called as

Multiple of b, b is called as factor/divisor or a.

• E.g: Given 24 and 6

• 6 is a divisor of 24

• 24 is a multiple of 6 .

• Give any multiples of 36

• 36 * 2 = 72, 36 * 3 = 108 ….

• Give any factors/divisors of 36

• 36/2 = 18, 36/3 = 12 …

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Common Multiple

• Common Multiple is a positive integer that is divided by all the given

numbers.

• E.g: Given 36, 48, 12 are three given numbers.

144 is the common multiple of the given numbers 36, 48, 12.

• E.g: If given three integers 15, 30, 75. Which of the following are the common

multiple of given three integers.

• 75

• 120

• 150

• 180

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Common Factor

• Common Factor is a positive integer when divided any of the given

numbers will give a remainder 0.

• E.g: Given 36, 48, 12 are three given numbers.

6 is the common factor. Is 12 also a common factor ?

• E.g: If given three integers 15, 30, 75. Which of the following are the common

factors of given three integers.

• 15

• 10

• 5

• 30

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Least Common Multiple

• Least Common Multiple is the smallest positive integer that is divided

by all the given numbers.

• E.g: Given 36, 48, 12 are three given numbers.

72 is the least common multiple of the given numbers.

• How to find the Least Common Multiple?

• Decompose the given numbers into prime factors.

• Separate all the common set of prime factors as one set and multiply with

rest.

• Explanation in the next page

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Least Common Multiple

• Find the least common multiple of 72, 96 and 120?

• Split each number into multiple factors.

• 72 = 3 * 3 * 2 * 2 * 2

• 96 = 3 * 2 * 2 * 2 * 2 *2

• 120=5* 3 * 2 * 2 * 2

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• LCM = 3 * 2 * 2 * 2 * 2 * 2 * 3 * 5 = 1440

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Great Common Factor/Divisor

• Great Common Factor/Divisor is the largest positive integer when

divided the given set numbers will give you the remainder 0.

• E.g. Given 36, 48, 12 are three given numbers.

12 is the Greatest Common Factor of the given numbers.

• How to find the Greatest Common Factor?

• Decompose the given numbers into prime factors.

• Separate all the set of common prime factors for each number and multiply

one set of common multiple factors.

• Explanation in the next page

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Greatest Common Factor/Divisor

• Find the greatest common factor of 72, 96 and 120?

• Split each number into multiple factors.

• 72 = 3 * 3 * 2 * 2 * 2

• 96 = 3 * 2 * 2 * 2 * 2 *2

• 120=5* 3 * 2 * 2 * 2

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• GCD= 3 * 2 * 2 * 2 = 24

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