Hi Lisa. The easiest way to determine the lowest denominator of a set of numbers is by grouping prime factors. I'll give you an example using different numbers so you can see how to do this with your own question.
Find the lowest common denominator for 18, 44, 41 and 121.
Start by listing the prime factors of each number. That is, find out what prime numbers you have to multiply together to get each number:
18 = 2 3 3
44 = 2 2 11
41 is prime, so we leave it.
121 = 11 11
The second step is to start the solution (call it S) with the first set of factors then add the "extra" factors from each of the other numbers:
Start with S = 2 3 3.
The next number is 44 = 2 2 11, but there is already one 2 in the expression for S, so cross it off and we are left with just 2 11. Now we append this to S:
S = 2 3 3 2 11
The next number is 41 = 41. Since there are no 41's in S, we append it:
S = 2 3 3 2 11 41.
The next number is 121 = 11 11. There is already one 11 in S, so we
only need to append the other 11 to S:
S = 2 3 3 2 11 41 11
We can write this in the form:
S = 2^{2} 3^{2} 11^{2} 41.
If you now multiply this out, you get 178596, which is the lowest common denominator for all four original numbers.
Here's one more example: What's the lowest common denominator of 7, 77, 84?
7 is prime
77 = 7 11
84 = 2 2 3 7
Start with the first line: S = 7.
The next expression is 7 11, but since there is one 7 already in S, we skip it and just add x 11 to S:
S = 7 11
The next expression is 2 2 3 7. There is already a 7 in S, so skip it and append the other factors:
S = 7 11 2 2 3 = 924. That's the lowest common denominator. Now try this method with your numbers. Here's a hint: there aren't any common prime factors in your set of numbers, so it's even easier that the examples I showed you.
Hope this helps,
Stephen La Rocque>
