Least Common Multiple and Greatest Common Factor

This week in Math we are learning about LCM and GCF. What on Earth are they, and what's so significant about them?? Well let me tell you, LCM is the Least Common Multiple, this is the smallest number that a pair or a group of numbers have in common. The Greatest Common Factor is the biggest number that goes into a pair or a group of numbers. This topic was a great review for me, I have learned it before but it has been a while and when I saw the topic come up I instantly had a brain block. I watched some videos that the teacher offered and I also found this video on my own. I think this video would be great for teachers to use for reference and also use if a student is struggling. 

Students love relating Math to the real-world, and I know that I do too. Any time that I can relate real-world with my Math examples I know I am able to help the students "connect the dots." Not only do I like to use real-world examples but I also like to help students "see" the problem, if I can use visual aids in a Math scenario I will. I like to be able to explain something and show something to help students really get what I am teaching. 

Here is a great GCF "real-world" scenario question for students:

Amanda has three pieces of cloth. One piece is 36 inches wide, another piece is 45 inches wide and the last piece is 54 inches wide. She wants to cut all pieces into strips of equal width that are as wide as possible. How wide should she cut the strips? 

Here is a great LCM "real-world" scenario question for students:

Jake runs every 10 days and Cleo every 6  days. Jake and Cleo both ran today. How many days will it be until they run together again?

 Both of the examples that I have given are good ways for students to "visualize" the problems. Students will be able to think about these problems in the future as they work out greatest common factor and least common multiple problems. Like I mentioned before I like to be able to show students problems that relate to the "real-world" and both of these do that.