Least Common Multiples

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What is the Least Common Multiple (LCM)?

The least common multiple of two or more numbers is the smallest number that is a multiple of all these numbers. To put it simply, it’s the smallest number that all the given numbers can divide into without leaving any remainder.

Finding the LCM

To find the LCM of two or more numbers, you list the multiples of each number and then find the smallest multiple they have in common.

Real-life Examples

  1. Race Track Laps: Imagine two friends, Alice and Bob, are running on a circular track. Alice takes 4 minutes to complete a lap, and Bob takes 6 minutes. You want to find out when they’ll both finish a lap at the same time. The LCM of 4 and 6 will give you this time. The multiples of 4 are 4, 8, 12, 16, etc., and the multiples of 6 are 6, 12, 18, etc. The smallest common multiple is 12. So, both will finish a lap together every 12 minutes.
  2. Baking Cakes and Cookies: Suppose you’re baking cakes and cookies. A cake takes 15 minutes to bake, and cookies take 10 minutes. To figure out when both will be done at the same time, find the LCM of 15 and 10. The multiples of 15 are 15, 30, 45, etc., and the multiples of 10 are 10, 20, 30, etc. The smallest common multiple is 30. So, both cakes and cookies will be done at the same time every 30 minutes.

Steps to Find the LCM

  1. List the Multiples: Write down the multiples of each number.
  2. Find Common Multiples: Look for multiples that are common to all the numbers.
  3. Identify the Smallest One: The smallest of these common multiples is your LCM.

Example of Finding the LCM

Let’s find the LCM of 8 and 12:

  • Multiples of 8: 8, 16, 24, 32, 40…
  • Multiples of 12: 12, 24, 36, 48…

The common multiples are 24, 48, etc., and the smallest of these is 24. So, the LCM of 8 and 12 is 24.

Why is the LCM Important?

In real life, the LCM is useful in situations where events with different cycles occur. It helps us figure out when these events will align or happen at the same time.

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