... Common Denominator?

When the denominators of 2 or an ext fractions room the same, they have actually Common Denominators.

You are watching: What is the least common multiple of the denominators for the two fractions 1/6 and 5/8?


... Least common Denominator?

it is the smallest of every the usual denominators.

Why?

Why execute we want typical denominators?

Because us can"t include fractions with different denominators:

13+16=?
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Before us can include them we need to make the denominators the same.

Finding a usual Denominator

But what must the brand-new denominator be?

One simple answer is to multiply the existing denominators together:

3 × 6 = 18

So instead of having actually 3 or 6 slices, we will make both of them have 18 slices.

The pizzas currently look like this:

618+318=918
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They currently have usual denominators (but no the least common denominator)

(Read an ext about common Denominators.)

Least common Denominator

That is every fine, however 18 is a many slices ... Can we do it v fewer slices?

Here is exactly how to find out:

13List multiples of 3: 3, 6, 9, 12, 15, 18, 21, ...
16List multiples that 6: 6, 12, 18, 24, ...

Now uncover the smallest number the is the same:

multiples that 3: 3, 6, 9, 12, 15, 18, 21, ...
multiples the 6: 6, 12, 18, 24, ...

The answer is 6, and also that is the Least common Denominator.

So allow us try using it!

We want both fractions to have actually 6 slices:

When we multiply top and bottom of 13 through 2 we get 26 16 currently has a denominator of 6

And our question currently looks like:

26+16=36
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One last step is to simplify the portion (if possible). In this situation 3/6 is simpler as 1/2:

26+16=36=12
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And the is what the Least typical Denominator is all about.

It allows us add (or subtract) fractions using the least number of slices.


What Did us Do?

The trick was to perform the multiples of every denominator, then uncover the Least usual Multiple

In the previous example the Least typical Multiple the 3 and 6 was 6.

In other words the Least common Denominator of 13 and 16 is 6.

Here are the steps to follow:

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Find the Least usual Multiple of the denominators (which is referred to as the Least common Denominator).Then include (or subtract) the fractions, together we wish!

Example: What is 16 + 715 ?

The Denominators are 6 and 15:

multiples that 6: 6, 12, 18, 24, 30, 36, ...
multiples 15: 15, 30, 45, 60, ...

So the Least usual Multiple of 6 and 15 is 30.

Now let"s try to make the platform the same.

Note: what we do to the bottom the the fraction, we must additionally do to the top

For the an initial fraction we can multiply top and bottom through 5 to obtain a denominator that 30:

× 5
16=530
× 5

For the second fraction we have the right to multiply top and also bottom by 2 to get a denominator that 30:

× 2
715=1430
× 2

Now we have the right to do the addition by including the top numbers:

530 + 1430 = 1930

The portion is currently as an easy as it have the right to be, so that is the answer.


Least common Multiple Tool

To find the least typical denominator immediately use the Least typical Multiple Tool. Simply put in the denominators, press the button, and also the least common denominator is shown.

One an ext Example


Example: What is 38 + 512?

List the multiples that 8 and also 12

multiples of 8: 8, 16, 24, 32, 40, ...

See more: Greenhouse Gas Containing Only Hydrogen And Oxygen ? Name A Common Greenhouse Gas Containing Only

multiples 12: 12, 24, 36, 48, ...

The Least usual Multiple is 24

For the an initial fraction we deserve to multiply top and bottom through 3 to acquire a denominator the 24:

× 3


38=924


× 3

For the second fraction we deserve to multiply top and bottom through 2 to acquire a denominator the 24: