What is the least common denominator of 15, 16, and 17?

Answer 1

Since there are no common factors; 15=3*5, 16=2^4 & 17 is prime; it is simply 15*16*17=4080

Answer 2

To find the least common denominator, simply list the multiples of each denominator (multiply by 2, 3, 4, etc.) then look for the smallest number that appears in each list.


Example: Suppose we wanted to add 1/5 + 1/6 + 1/15. We would find the least common denominator as follows...

First we list the multiples of each denominator.

Multiples of 5 are 10, 15, 20, 25, 30, 35, 40,...

Multiples of 6 are 12, 18, 24, 30, 36, 42, 48,...

Multiples of 15 are 30, 45, 60, 75, 90,....

Now, when you look at the list of multiples, you can see that 30 is the smallest number that appears in each list.

Therefore, the least common denominator of 1/5, 1/6 and 1/15 is 30.

This method works pretty good. But, adding fractions with larger numbers in the denominators it can get pretty messy.


So hold that thought for a moment, as we look at another way to find a least common denominator for adding these same fractions.

Answer 3

1

Answer 4

17 is a prime number so it must be 1. But then all combinations numbers have a least common denominator of 1 as all numbers can be divided by one and still give an integer value. For these three, however, 1 is also the greatest common denominator, which is probably what you meant

Answer 5

I think you need to understand your terminology better first!

The LCD (least common denominator) of these numbers is 1, but I doubt that's what you were really asking about.

You are probably asking for the least common multiple which, since none of these numbers have any prime factors in common, would simply be 15 * 16 * 17 = 4,080

Better spend more time studying and less time on YA, young lady!

Answer 6

Because those number do not share any divisor besides 1 (17 is prime, 16 is 2*2*2*2 and 15 is 3*5), then the smallest number can can be divided by those values without remainder is the product of all 3 values, 15*16*17, or 4080

Answer 7

Actually the typical item that people look for are GREATEST common denominator and LEAST common multiple.

And yes the greatest common denominator is 1

Answer 8

well if you are looking for the LCD and not the LCM you have to turn each of them into improper fractions 15/1 16/1 and 17/1 so the LCD would be 1

Answer 9

multiply all of them to get it because none of them go into one another, 17 is a prime number so the least common denominator is determined by multipling them all

Answer 10

are u sure u don't mean "greatest common denominator" or "least common multiple"? after all, the least common denominator for any set of numbers is 1...