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.
Aug 09, 16 01:40 PM
Average age of Dipu and Apu is 22 years. Average age of Dipu and Tipu is 24 years. Age of Dipu is 21 years. What are the ages of Apu, and tipu ? Let
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