Question 1170228
<br>
Well........<br>
You have received three responses to this point.<br>
The first used prime factorization; but to me the presentation is not very clear.<br>
The second did not use prime factorization; it used a more elementary (and therefore, in general, less useful) method.<br>
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.....!)<br>
So here is my attempt to show what you were asking for.<br>
(1) Find the prime factorizations of each denominator:
6 = 2*3
8 = 2*2*2
4 = 2*2<br>
(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:<br>
LCM = 2*2*2*3 = 24<br>
Now convert each of the given fractions to an equivalent fraction with a denominator of 24 and solve the problem.<br>
{{{1/6+3/8+1/4 = (1*4)/(6*4)+(3*3)/(8*3)+(1*6)/(4*6) = 4/24+9/24+6/24 = 19/24}}}<br>
Then the fraction of the pie that was left was<br>
{{{1-19/24 = 24/24-19/24 = 5/24}}}<br>