# Lowest Common Multiple - LCM

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1. May 4, 2015

### matqkks

What is the most motivating way to introduce LCM of two integers on a first elementary number theory course? I am looking for real life examples of LCM which have an impact. I want to be able to explain to students why they need to study this topic.

2. May 4, 2015

### symbolipoint

Most elementary school students being children, do not have significant, conscious, mathematical experience to make applications meaningful to them. This could be why, in case you get few responses, that few responses may occur for your question. Food recipes sometimes serve as simple examples.

3. May 4, 2015

### Delta²

Well you could tell them that number theory is used in cryptography, cryptography is used in web sites on the inet to make the web page secure (to prevent or make it much harder for our criticial pieces of information like passwords and other data to fall into the wrong hands), so maybe that will make them to show more interest on the topic.

4. May 4, 2015

### Staff: Mentor

I'll take a shot at it (pun intended with my example). Suppose I am an unscrupulous bartender who wants to water down a fifth of vodka (1/5 of a gallon) with a quart of water (1/4 of a gallon). How much watered-down vodka will I get?

5. May 4, 2015

### HallsofIvy

Adding fractions with different denominators is the most basic application of "least common denominators" and certainly you should be able to give may "real world" applications of adding and subtracting fractions.

6. May 4, 2015

### CWatters

Perhaps look for problems that imply the solver gets a reward..

You are able to go to a park every n days. On one visit you meet a really good looking girl (or famous person). She/he tells you they are only able to go to the park every m days on their day off. Unfortunately you loose their phone number on the way home - how many days do you have to wait before you can meet them in the park again?

You are able to go to the park every n days. On one visit you meet some kids scrambling around picking up sweets/gold coins. They tell you that it falls out of a lorry that goes past every m days. The other kids plan to come back in x days time. Is there a better plan?

7. May 4, 2015

### CWatters

Two planets orbit the sun, one every x years and one every y years. The inhabitants of planet x discover they have just missed a close encounter with planet y. When is their next opportunity/encounter?

Real life problem ... Voyager spacecraft. Planets align every 175 years.