Kristiangabawa
Answered

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Find the first three common multiples and LCM of 16. 12. And 8.

Sagot :

LesterDC

Hi Kristiangabawa,

Multiples and factors are somehow relevant with each other. They both use multiplication but on different methods.

Factors are numbers through which we use in order to get the result (product).

However, multiples are results of multiplying a certain number to another number (multiple). Let me demonstrate this with the use of an example:

Suppose we have the number 10:

The factors of the number 10 are 2 and 5. Simply because by definition of a factor, if we multiply 2 and 5 we will get 10.  

 [tex]2 x 5 = 10[/tex]

On the other hand the multiples of 10 are 10, 20, 30, 40, and so on. We get those numbers by just multiplying 10 to a certain sequence of numbers (1, 2, 3, 4,…). Here’s an short example on how did we got this

 [tex]10 x 1 = 10[/tex]

 [tex]10 x 2 = 20[/tex]

 [tex]10 x 3 = 30[/tex]

 [tex]10 x 4 = 40[/tex]

Just a hint:

Factors are finite, while multiples are infinite.

Now for your problem:

In order to get the least common multiple of two numbers we could use a common multiples calculator or by listing all the possible multiples and comparing as to which is common among them. Let’s take an example of getting the common multiples of 2 and 3

Multiples of 2

[tex]2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30[/tex]

Multiples of 3

[tex]3, 6, 9, 12, 15, 18, 21, 24, 27, 30[/tex]

If you look closely, the numbers that is common among the multiples of 2 and 3 are the following;

[tex]6, 12, 18, 24, 30[/tex]

Take a look back again to check it, (I bet you will)

Now the least common multiple of 2 and 3 is the number that has the lowest value. Among the list above, we have the number 6. Thus 6 is the LCM of 2 and 3.

If we get the first three common multiples of 16, 12 and 8 we will be doing the same thing we have made a while ago. But instead of looking the number of the lowest value, we will get three numbers that has the lowest value. Here’s how;

1. List down the multiples of the number. Make it as long as it should (because multiples are infinite)

  Multiples of 16 = 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240, 256, 272, 288, 304, 320

 Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240

 Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160, 168, 176, 184, 192,  200, 208, 216, 224, 232, 240

 2. Now look for the number that is common among the numbers 16, 12 and 8. We have

 Common multiples = 48, 96, 144, 192, 240

 3. Among the list above the numbers of the lowest values are 48, 96 and 144

Hence, the first three common multiples of 16, 12 and 8 are 48, 96 and 144.

You can try it yourself by getting the common multiples of 3 and 8 less than 50. It will be beneficial for you to practice to sharpen your edge in math.

To understand more about multiples click on these links.

brainly.ph/question/893968

brainly.ph/question/244475

brainly.ph/question/1650472

Hope this helps!


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