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Greatest Common Factor (GCF) and Least Common Multiple (LCM)

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Prime Factorization Prime Factorization is when a number is expressed as a product of prime factors. You can use a factor tree to find the prime factorization of a number. Example: Find the prime factorization of 12. 12 26 232

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Factoring Monomials You can use prime factorization to factor monomials. A monomial is in factored form when it is expressed as the product of prime numbers and variables and no variable has an exponent greater than 1. Example: Factor 100mn 3. 100 10 5252 mn 3 = mnnn

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Finding a GCF through Reasoning Find the greatest common factor of: 8, 28, 12 Factors of 8: Factors of 28: Factors of 12: 1248 12471428 1234612 Find the largest number that divides all three numbers. The GCF is 4. This process could be long and tedious if the numbers are large. A more efficient method is desirable.

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Greatest Common Factor (GCF) The Greatest Common Factor (GCF) is the greatest expression that is a factor of the original expressions. Procedure to find the GCF of two or more terms: 1.Factor each monomial. 2.The GCF is the product of the common factors.

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Examples Find the GCF of each set of monomials: a)24, 60, and 72 b)15 and 8 c)15 a 2 b, 9 ab 2, and 18 ab Step One: Factor each Monomial. Step Two: Find the common factors. Step Three: Multiply the factors in common. There is nothing in common, so the GCF is…

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Finding a LCM through Reasoning Find the least common multiple of: 8, 28, 12 Multiples of 8: Multiples of 28: Multiples of 12: 816243240485664 72808896104112120128 136144152160168176184192 285684112140168196224 1224364860728496 108120132144156168180192 Find the smallest number that is a multiple of all three. The LCM is 168. This process could be long and tedious if the numbers are large. A more efficient method is desirable.

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Least Common Multiple (LCM) The Least Common Multiple (LCM) is the least number that is a common multiple of two or more expressions. Procedure to find the LCM of two or more terms: 1.Factor each monomial. 2.Find the greatest number of times each factor appears in each factorization. 3.The LCM is the product of (2).

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Examples Find the GCF of each set of monomials: a)18, 30, and 105 b) 15 a 2 b and 27 b 3 Step One: Factor each Monomial. Step Two: Find the greatest number of times each factor appears in each factorization. Step Three: Multiply the result of (2).

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