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.
2026-02-23 23:01:51.1771887711
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Why study Lowest Common Multiple - LCM
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Alice hit the bulls eye 43 times in 57 attempts; and Bob hit it 48 times in 61 attempts. Who has a good record? Ideally to make them comparable both should have made an equal number of attempts. So we scale them up by maintaining hit rate by expressing the success count for the same number of hits; this requires a common multiple. For economy least common multiple makes sense.
A real life example of finding LCM is adding two fractions together:
$$\frac14+ \frac16 = \frac3{12} + \frac2{12} = \frac{5}{12}$$
How do you know what the common denominator is? Well, it's the LCM of all of the denominators.