I often get asked the question, why do students need to learn how to find the LCM of two or more numbers. I can only think of two mathematical examples, the first is to find common denominators for fractions so that we can add the fractions more easily. For example, if we have the fractions 1/4, 1/3, and 1/6, we could use the LCM to create equivalent fractions to add quickly and easily.
The second reason is to solve real-world problems. If two or more events are happening at different time frames and we want to know when they both will happen at the same time. For example: Hot dogs come in eight-packages and hot dog buns come in six per package. How many Hot dogs and buns do I need to buy to have the same amount? How many packages of each would that be? I like to use story problems to find the LCM, real-world story problems helps students with the question of "why do I need to know this". The attached PDF gives many examples of story problems where finding the LCM is the focus.
Now that I have shared the why, let's look at the how.
Step #1: Students need to define, in their own words, each word in this mathematical term. "Least", what does this mean? Students may define it as smallest in quantity, little, etc. Record the students' ideas on the board. What does "Common" mean? Students may come up with frequent, general, have the same, etc. Record ideas on board. What does "Multiple" mean? The answers as a result of skip counting. Ask students to provide examples. Multiples of three are: 3, 6, 9, 12, 15...
Step #2: Give students a real-world example and ask them to solve. Jeremy has a soccer game every 4th day, Matt has one every 6th day. When will they have a game on the same day? Ask students to share their thinking. If students do not have an organized way of expressing their thinking, introduce an open number line. Use the open number line to skip count to find the Least Common Multiple. For students who need more structure than an open number line, use a hundreds chart to find LCM.
Step #3: Give students real-world problems to solve. Be certain to have students share out their thinking. A lesson plan that I used in a 5th grade classroom can be found below. If you have any questions or suggestions of how you have taught Least Common Multiple, please email me at firstname.lastname@example.org