This lesson will teach you 3 methods for finding the least common multiple(LCM) of two whole numbers. We will start with a definition of the word multiple.
The multiples of a number are the answers that you get when you multiply that number by the whole numbers except 0.
Remember that the whole numbers are all numbers from 0 to infinity
whole number = {0, 1, 2, 3, 4, 5, 6, 7, 8,........}
So multiply any number 1, 2, 3, 4, 5, 6, 7, 8,........ to get the multiples of that number.
For instance, you get the multiples of 4 by multiplying 4 by 1, 2, 3, 4, 5,....
I put the dots to show that the sets of whole numbers continues forever.
The answer is { 4, 8, 12, 16, 20, .....}
In the same way, the multiples of 9 are all the numbers that you get when you multiply 9 by 1, 2, 3, 4, 5, 6,.....
After you do that, you will get { 9, 18, 27, 36, 45, 54,....}
The LCM of two numbers is the smallest number that is a multiple for both numbers.
Method #1: Set intersection method:
Example: Find LCM of 6 and 9
First list all the multiples of 6
You get {6, 12, 18, 24, 30, 36, 42, 48, 54, 60,....}
Next,list all the multiples of 9
You get {9, 18, 27, 36, 45, 54, 63, 72, 81, 90....}
Pull out all the common multiples or find the intersection of the two sets
The common multiples are {18, 36, 54,.....} Looking at the list of common multiples immediately above, you can see that the smallest number that is a multiple of both 6 and 9 is 18.
Of course, 36 is also a common multiple of 6 and 9. However, it is not the smallest common multiple.
Example: Find LCM of 2 and 3
Multiples of 2 are {2, 4, 6, 8, 10,....}
Multiples of 3 are {3, 6, 9, 12, 15....}
The least common multiple of 2 and 3 is 6
You can also write LCM(2,3) = 6
Method #2: My teacher's method: find LCM( 6, 9) and LCM (120, 180)
Technique:
Start by dividing each number by 2. (If 2 does not work, start with 3 instead, and so forth)
Keep dividing by 2 until 2 does not work anymore
When 2 does not work anymore, divide by 3
When 3 does not work anymore, divide by 4
Keep doing this until you can no longer divide
LCM = The product of all the numbers on the left of the red line.
Take the quiz below to see how well you understand the LCM.
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