Many 5th and 6th graders (and their parents!) struggle with understanding the concept of lowest common multiple, often referred to as LCM for short. If you are one of them, don’t worry, we are here to help.
Understand the meaning behind the vocabulary
The least or lowest common multiple means of all the common multiples, the number which is the smallest. Let’s start by tackling one word and concept at a time.
A multiple is a product of multiplication. The multiples of 9 are: 9, 18, 27, 36 and so on. The lowest multiple is simply the smallest multiple of any number. So the lowest multiple of any number is that number times 1. 1 x 9= 9 so 9 is the lowest multiple of 9. It gets more interesting when you say common multiple. The word “common” means the same. If you have a set of numbers, each number in the set will have different multiples. As an example, let's use the set of numbers (3, 9, and 10).
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60 … 90, 93, and so on.
Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, and so on.
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120 and so on.
The common multiples of 3 and 9 are the numbers that are in both sets of multiples including 9, 18, 27, 36, 45, 54, and so on.
Any multiple of 9 is also a multiple of 3.
A common multiple of 9 and 10 is 90 (and also 900 and 9,000).
The common multiples of the set (3 and 10) are 30, 60, 90, 120 and so on. Only 30 is the LCM because it is the smallest possible common multiple.
The common multiples of 3, 9, and 10 are 90, 900, 9,000 and so on, and of those 90 is the LCM because it is the smallest possible common multiple for all three numbers in our set.
Finding the LCM
Therefore, the least common multiple or LCM of the set (3, 9, and 10) is 90 because it the smallest number that every number in the set evenly divides into.
To determine the LCM, you could find all the multiples of all the numbers in the set (like we did above) and then just see which number is the lowest common multiple. That works pretty well with small numbers and small sets like 3 and 5
Multiples of 3: 3, 6, 9, 15, 18
Multiples of 5: 5, 10, 15, 20.
It’s obvious within a few seconds that 15 is the least common multiple of 3 and 5.
Isn’t there a better method?
Listing all the multiples isn’t always reasonable to find the LCM. It can get too time-consuming and difficult. There are several other methods. These methods use “prime factorization”. These strategies are great for kids who have a solid understanding of LCM and why prime factorization strategies work. But jumping to a shortcut too soon can be detrimental to understanding.
If you (or your kid) needs help understanding prime factorization or LCM, bring them by Mathnasium of Parker for their free trial session. Appointments are required for free trial sessions, so please call ahead to make sure we are ready for you! 303-840-1184
This article was written by and owned by Cuttlefish Copywriting, www.cuttlefishcopywriting.com . It is copyright protected. Mathnasium of Parker has permission to use it. Other Mathnasium locations should contact Heather at [email protected] before using it.
