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Prime Factorization GCF LCM LCD Prime Factorization Factor Tree Break a number down into all the prime factors of that number What prime numbers multiplied together give you your original number Write repeated multiplication with exponents Example 12 12 2 2 3 2 3 2 2 6 2 3 Lowest Common Multiple Also known as lowest common denominator What is the smallest number 2 or more numbers can both be multiplied into 2 Methods 1. List all the multiples of the numbers and find the smallest one they have in common 2. Do the prime factorization of each number, write each number once, take the largest exponent Example 18 2 3 2 24 2 3 3 LCM 2 3 72 3 2 Greatest Common Factor What is the largest number all can be divided by evenly. 2 ways 1. List all the factors of each number, find the largest one they have in common 2. Find the prime factorization of each number, write only prime numbers they all have in common and take the lowest exponents Example 36 3 2 30 2 3 5 GCF 2 3 6 2 2 GCF if Variables are involved Take variables that are common in all terms Lowest exponent on the variables 18 x 3 y 2 32 24 x y 2 3 2 2 3 GCF 2 3 x 2 y 6 x 2 y