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## Greatest Common Factor and Least Common Multiples GCF and LCM

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**Greatest Common Factor and Least Common MultiplesGCF and LCM****There are actually 3 ways. You can use prime factorization,**write out all the prime factors for each number or extract common prime numbers.**List the factors of 60:1,2,3,4,5,6,10,12,15,20,30,60List the**factors of 961,2,3,4,6,8,12,16,24,32,48,96find the largest factor - 12**…or do prime factorization. Circle all the primes the 2**numbers have in common and multiply one set of them to get your GCF. 96 60 48 2 2 30 24 2 15 2 12 2 3 5 6 2 2 x 2 x 3 = 12 2 3**…or you can extract the common prime factors of 60 and 96**and form a product to give the GCF. This, to me, is the easiest way. Try it! 2 60, 96 2 x 2 x 3 = 12 2 30, 48 3 15, 24 5, 8**96**24 36 48 2 2 12 18 2 24 2 6 9 2 2 12 2 3 2 3 3 6 2 144 2 3 12 12 3 4 2 x 2 x 3 = 12 3 4 2 2 2 2**2**36, 24, 144, 96 2 x 2 x 3 = 12 2 18, 12, 72, 48 3 9, 6, 36, 24 3 2 12 8**There are 3 ways to find the LCM as well. You can list the**multiples of the numbers, do prime factorization, or extract the prime factors from either one or both numbers.Find the LCM of 12 and 18**Multiples of 12 are…12,24,36,48,60,72,….Multiples of 18**are…18,36,54,72,90,108,…The smallest multiple the 2 numbers have in common is the least common multiple.**…or do prime factorization. Write down the number they**have in common only once, then write down the leftover numbers. Multiply them all together. 12 18 9 4 2 3 3 3 2 2 Numbers in common are 2 and 3 Leftover numbers are 2 and 3 2 x 3 x 2 x 3 = 36**Remember…the numbers you pull out have to be prime**numbers! 2 12, 18 2 6, 9 3 3, 9 3 1, 3 1 1 2 x 2 x 3 x 3 = 36**245**35 420 42 5 49 10 5 7 5 7 7 2 6 7 2 3 Numbers they have in common: 5 and 7 Leftover numbers: 2, 3, 2, 7 Multiply them all together: 5 x 7 x 2 x 3 x 2 x 7 = 2940**primes**5 35, 420, 245 7 7, 84, 49 7 1, 12, 7 3 1, 12, 1 2 1, 4, 1 2 1, 2, 1 1, 1, 1 5 x 7 x 7 x 3 x 2 x 2 = 2940**7 28 63 4 9**GCF = 7 LCM = 7 x 4 x 9 = 252**1 12 13**GCF = 1 LCM = 1 x 12 x 13 = 156**3 27 21 33 15 9 7 11 5**GCF = 3 LCM = 3 x 9 x 7 x 11 x 5 = 10,395