Being able to determine the greatest common factor GCF and least common multiple LCM of a set of numbers is a very useful skill. To find either the LCM or the GCF of two or more numbers, you start the same way: begin with prime factorization of all numbers. You then compare and contrast what you need. To find GCF, multiply all prime factors that are shared between the numbers including repeating common factors. We then look for shared factors in order to find GCF.
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At this point, students should have a high level of understanding of factors, multiples, composite and prime numbers. I will give them the below problem to challenge their ability to use multiple concepts to problem solve. If a student is struggling with the problem, I will suggest that they look at each clue individually and then determine where the answers may overlap. After about 10 minutes, I will reconvene the class and we will discuss the strategies they used to find the number.