What is a common denomonator for 5 3 4 and 2?

Answer 1

5,3,4, and 2 have many common denominators. What is the least common denominator of all of them?

Let's look at the multiples of each number. We do this because common denominators are really common multiples of the denominators. And the LCD is really just the least common multiple (LCM) of the denominators.

Starting with 2, the 3, and 4 and last 5 we have the following lists of multiples:

2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,68,60

3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60

4,8,12,16,20,24,28,32,36,40,44,48,52, 56,60

5,10,15,20,25,30,35,40,45,50,55,60

So 60 is the first common multiple and it is the least common denominator of 2, 3, 4 and 5. Note that we could also factor 2, 3, 4 and 5 into primes (2, 3 and 5 already are) So we have 2, 3, 2^2 and 5 We take the largest exponent possible from each and we have 3 x 2^2 x 5 = 20 x 3 = 60. This is the faster way to do this.