Secondary I • 3yr.
My teacher tells me that to work on fractions, it is useful to master LCM. How can I find it? I have heard of multiples and trees.
My teacher tells me that to work on fractions, it is useful to master LCM. How can I find it? I have heard of multiples and trees.
Explanation from Alloprof
This Explanation was submitted by a member of the Alloprof team.
Good evening,
The multiples method and the factor tree method are indeed used to find the LCM! There is a third technique, the table, but let's tackle the ones you mentioned!
1. Method of multiples.
To find the LCM, we first make a list of the multiples of each number.
Suppose the numbers 6, 9 and 12.
The multiples of 6 = {6, 12, 18, 24, 30, 36, 42, 48,…}
The multiples of 9 = {9, 18, 27, 36, 45, 54 , 63, 72,…}
The multiples of 12 = {12, 24, 36, 48, 60, 72, 84, 96,…}
We observe that 36 is the lowest common multiple!
2. Factor tree method.
Find the LCM of two numbers:
We decompose the two numbers using a factor tree until we get only prime factors. Common factors and unique factors are identified.
Example 9 and 12.
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We get 9 = 3 x 3.
We get 12 = 2 x 2 x 3.
The common factor (in orange) is 3.
The unique factors (in blue) are 3, 2 and 2.
The common factors are multiplied by the single factors.
So 3 x 3 x 2 x 2 = 36 which is the LCM.