SOLUTION: One elf ate 1/6 of a pie. Another elf ate 3/8 of the pie. A third elf ate 1/4 of the pie. How much of the pie was left? Show how you found the common multiple using prime facto

Question 1170228: One elf ate 1/6 of a pie. Another elf ate 3/8 of the pie. A third elf ate 1/4 of the pie. How much of the pie was left?
Show how you found the common multiple using prime factorization, then solve.
I'm stuck! Please help!

Found 4 solutions by josgarithmetic, MathLover1, ikleyn, greenestamps:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Start is from one whole pie, 1 pie.

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One elf ate 1/6 of a pie. Another elf ate 3/8 of the pie. A third elf ate 1/4 of the pie.
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How much is still uneaten?

Look at the denominators.
6, 8, 4.
If you are trying to use prime number factorizations to find the lowest common denominator, then:
2*3, 2*2*2, 2*2;
You need 1 of 3 factor and 3 of 2 factor
which is , which is same as 24.

Raise all your terms to higher terms of denominator 24.
--------now compute this, and simplify if possible.
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

let whole pie be
One elf ate of a pie
Another elf ate of the pie
A third elf ate of the pie
then

write down
the multiples of
the multiples of
the multiples of
the common multiple:
=
=
=
=
How much of the pie was left?
answer: of the pie was left

Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.

If you learn about the Least Common Multiple from the formal point of view,
you probably NEVER will get real understanding.

Actually, in the most simple cases, with which you will have deal in school, you can find LCM mentally and intuitively,
based on your common sense: LCM is   a common multiple and the   least common multiple

LCM(2,4) = 4 LCM(2,3) = 6 LCM(3,4) = 12 LCM(4,5) = 20 LCM(3,6) = 6 ( <<<---=== I fixed my typo here . . . ) LCM(3,8) = 24 LCM(5,6) = 30

It is practically all you need to know.

If you know it, your common sense will do the rest and will guide you.

The formal definition is needed only to work with complicated cases, which you, probably, will never meet is your school practice.

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Well........

You have received three responses to this point.

The first used prime factorization; but to me the presentation is not very clear.

The second did not use prime factorization; it used a more elementary (and therefore, in general, less useful) method.

And the third response dismissed the problem, saying you would never need formal math to find the common denominator, because the only examples you will ever see in your classroom are ones that can be found using common sense. (And then they show a few examples, one of which is wrong.....!)

So here is my attempt to show what you were asking for.

(1) Find the prime factorizations of each denominator:
6 = 2*3
8 = 2*2*2
4 = 2*2

(2) The least common denominator has to consist of each prime factor the largest number of times it occurs in any one of those factorizations.
There is one factor of 2 in 6; three factors of 2 in 8; and two factors of 2 in 4. So the LCM must contain three factors of 2.
There is only one 3 in any of the factorizations, so the LCM contains one factor of 3.
There are no other prime factors. So the LCM contains three factors of 2 and one factor of 3:

LCM = 2*2*2*3 = 24

Now convert each of the given fractions to an equivalent fraction with a denominator of 24 and solve the problem.

Then the fraction of the pie that was left was

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