what is the common denominator to 3/5, 1/3, and 1/6
Let's look at the multiples of these denominators.
5, 10, 15, 20, 25, 30, 35, 40
3, 6, 9, 12, 15, 18, 24, 27, 30, 33, 36, 39
6, 12, 18, 24, 30, 36, 42, 48, 54
What is the smallest number that appears in all three lists of multiples?
That's the lowest common denominator.
You want the least number which contains all the prime factors of 5,3 and 6.
Since 6 = 2*3, it already contains 3.
So, you want the smallest number that contains all the factors of 5 and 6. That would be 30.
Try another example.
The LCD of 6 and 15 and 12 would be found by listing the factors of each:
6=2*3
15=5*3
12=2*2*3
So, you need 2*2*3*5 to contain all of those factors. 2*2*3*5 = 60. You can see that 6,12,15 all divide 60 but not any smaller number.
6/60=10
12/60=5
15/60=20
To find the common denominator among fractions, you need to determine the least common multiple (LCM) of the denominators. The LCM is the smallest number that all the denominators can divide into evenly.
First, let's list the multiples of each denominator:
Multiples of 5: 5, 10, 15, 20, 25, 30, ...
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, ...
Multiples of 6: 6, 12, 18, 24, ...
From these lists, we can see that the least common multiple of 5, 3, and 6 is 30. Therefore, 30 is the common denominator for the fractions 3/5, 1/3, and 1/6.