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Least Common Multiple



This lesson will teach you a method 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

Remember that the whole numbers are all numbers from 0 to infinity

whole number = {0,1,2,3,4,5,6,7,8,........}

Example: You get the multiples of 4 by multiplying 4 by 0,1,2,3,4,5,....

I put the dots to show that the sets of whole numbers continues forever.

The answer is { 0, 4, 8, 12,16, 20, .....}

Example: the multiple of 9 are all the numbers that you get when you multiply 9 by 0,1,2,3,4,5,6,.....

After you do that, you will get {0,9,18,27,36,45,54,....}

The LCM of two numbers is the smallest number that is a multiple for both numbers.

Example: Find LCM of 6 and 9

First list all the multiples of 6

You get {0,6,12,18,24,30,36,42,48,54,60,....}

Next,list all the multiples of 9

You get {0,9,18,27,36,45,54,63,72,81,90....}

Carefully examine the two list and you will 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.

Example: Find LCM of 2,and 3

Multiples of 2 are {0,2,4,6,8,10,....}

Multiples of 3 are {0,3,6,9,12,15....}

The least common multiple of 2 and 3 is 6

You can also write LCM(2,3) = 6




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