Posted by Kim on Tuesday, May 28, 2013 at 4:48pm.
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