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A review sheet on finding the least common multiple (lcm) and greatest common factor (gcf) of numbers. It explains the concepts of lcm and gcf, provides examples, and offers steps to find the lcm and gcf of given sets of numbers. The document also discusses the relationship between lcm and gcf.
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Name: _________________________________ Date ____________________ LCM, GCF, Prime Factorization Review Sheet LCM: The Least Common Multiple is the smallest multiple that two or more numbers divide into evenly. A multiple of a number is the product of the original number with another number. Some multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, … Some multiples of 7 are 7, 14, 21, 28, 35, 42, 49, 56, … A Common Multiple is a number that is divisible by two or more numbers. Some common multiples of 4 and 7 are 28, 56, 84, and 112. When looking for the Least Common Multiple, you are looking for the smallest multiple that they both divide into evenly. The least common multiple of 4 and 7 is 28. To find least common multiples, you should break all numbers down into their prime factorization. First consider the COMMON factors they all contain. And then use all the “LEFTOVER” factors. By multiplying all these factors together, you will produce the LCM. The prime factorization of 4 is 2• 2 The prime factorization of 7 is 7 Since there are no common factors, use all the factors (what I call the “leftovers” ), and multiply them together to produce the LCM, which is 28. Find the LCM for the following sets of numbers. 24 and 42 36 and 60 LCM: LCM:
To find least common multiples, you should break all numbers down into their prime factorization. First consider the COMMON factors they all contain. When there are more than two numbers, also consider the COMMON factors that some of the numbers contain. And finally, use all the “LEFTOVER” factors. By multiplying all these factors together, you will produce the LCM.
LCM and GCF Complete: The similarity between LCM and GCF_______________________________________ The difference between LCM and GCF ____________________________________________________ Definition: A number is prime only if 1 and itself are factors. The number is prime if it is only divisible by 1 and itself. List of prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, … Prime Factorization. Find all the prime numbers that were Multiplied together to produce the original number. In other words, break down the original number into factors. Continue to break down the factor so that all that is left is prime number. Find the prime factorization of 28. 28 2 14 28 = 2• 2 • 7 2 7 36 153 120