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

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

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

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

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.

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.

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…

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.

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).

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).