Expert: Scott A Wilson - 11/2/2009

Question
Hi Scott,

I wanted to know as to how we calculate LCM of fractions??
for example finding the LCM of 2/3 and 3/4??
Also if you could explain the logic behind the method...it would be great


Thanks,
Shikhin

Answer
To determine the best denominator with fractions, determine the LCM of the denominators.

The lowest number that 2/3 could be multiplied by to get an integer would be 3.
The lowest number that 3/4 could be multiplied by to get an integer would be 4.

The LCM of 3 and 4 is 12, since there is no other samller that 3 and 4 both go into.

But back to what is at hand.

2/3 = 8/12 and 3/4 = 9/12, so 2/3 + 3/4 = 8/12 + 9/12 = 17/12 = 1 5/12.

If the denominators were 6 and 4, the number to use would still be 12.
If the denominators were 18 and 28, the prime factors would be looked at.
It is known that 18=2*3*3 and 48=2*2*2*2*3.
From here, it can be seen the number needs to have 4 2's and 2 3's/
That is, 2*2*2*2*3*3 = 16*9 = 144.
This means that the numbers in 18ths would need to be multiplied by 9/9 since 18*9 =144.
It would also mean the number in 48ths would be multiplied by 3/3, since 3*48 = 144.