LOWEST COMMON MULTIPLE (LCM)
As we discussed in our previous post, so shall we discuss here. We talked about HCF which stands for Highest Common Factor. We know you can only solve when you have the factor that is common in all given numbers. But LCM here is a different scenerio.
We already know what a factor is, in terms of HCF.
Now, let's talk about multiple, in terms of LCM.
ueir efore we delve deeper into LCM, let's understand multiples to the fullest. Just like we understood factors
What is Multiple? Oo 9 of off
Multiple of a given number are numbers that are formed by successfully multiplying the given number by counting number, 1, 2, 3, 4, 5, 6,....
Example
Multiples of 3 and 5 are found here
Multiples of 3 are 3 x 1 = 3, 3 x 2 = 6, 3 x 3 = 9, 3 x 4 = 12,....
Multiples of 5 are 5 x 1 = 5, 5 x 2 = 10, 5 x 3 = 15, 5 x 4 = 20,....
The multiples of 3 are 3, 6, 9, 12,...and so on.
The multiples of 5 are 5, 10, 15, 20,...and so on.
NB: best way to find multiples is adding the given number by itself.
i.e Multiples of 3 are 3, (3 + 3)=6, (6 + 3)=9, (9 + 3)=12, ... and so on.
Unlike Factors, Multiple doesn't have end. Keep adding till thy kingdom come, you're free.
Now that we have broad knowledge on Multiples, lets delve deeper into LCM itself.
METHOD I
Example I
Find the LCM of 2 and 3
Solution
NB: we use mutiples to find LCM while factors to find HCF
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20,...
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30,...
If you look closely, you can see there are numerous numbers that are common in both multiples. We can see 6, 12, 18,.... appeared in both multiples. But, the Lowest Common Multiple is 6.
Therefore, LCM of 2 and 3 is 6
Example II
Find the LCM of 10, 15 and 30
Solution
Multiple of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100,...
Multiples of 15: 15, 30, 45, 60, 75, 90, 105,....
Multiple of 30: 30, 60, 90, 120, 150, 180,....
The common factors of 10, 15 and 30 are 30, 60, 90,..and so on. But the Lowest Common Multiple is 30.
METHOD II
Find the LCM of 10, 15, and 30
Here, we don't use Multiples, we use prime factors. As the name implies, LCM, you use the lowest number that can divide any of the given number. Here, the lowest number that can divide any of the given number is 2
NB: check the image below for simplified calculations
Want to know more about HCF and LCM? Then stick with us till the end.
Check out our previous lesson on HCF
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LCM