What is the least common denominator of 3/20 and 8/15?

Question

Please help!

Answer 1

20=2x2x5

15=3x5

you are finding the least common multiple of 15 and 20

first write the prime factorization for each number (as you can see)

take all of the first number's prime factors

you want 2x2x5 so far...

now take all of the second number's prime factors that you don't already have !!!

from the second number we already have the 5 so we don't need it

from the second number take the 3 because we don't have any 3s

LCM=2x2x5x3=60 is the LCM or LCD

another solution is...

20={20,40,60,80,100,...}

15={15,30,45,60,75,90,...}

what is the smallest number common to both sets ?

you're right ! 60

Answer 2

First factor both denominators into primes:

 

20 = 2 · 2 · 5

15 = 3 · 5

 

The common denominator (s····ame as the least common multiple - LCM) must contain at least one of each different factor. 

 

So the LCM must have at least 2 · 3 · 5

Since the "2" appears twice in the 20, it must appear twice in the LCM.

 

LCM = 2 · 2 · 3 · 5

LCM = 60