What is the LCD of 18 , 30 , 72 ?

Question

What is the LCD of 18 , 30 , 72 ?

Answer 1

Factoring them is the easiest way to figure this out.

18 = 2 * 3^2

30 = 2 * 3 * 5

72 = 2^3 * 3^2

So the lowest common denominator will be:

2^3 * 3^2 * 5 = 8 * 9 * 5 = 72 * 5 = 360, because that combines the highest powers of every prime decomposition.

Answer 2

2

Answer 3

To find an LCD of a set of numbers, take the the prime factorization of each number, and multiply the individual prime numbers to the greatest power of that prime in the set, by every other prime of greatest power in the set.

Factor 18

2^1 * 3^2

Factor 30

2^1 * 3^1 * 5^1

Factor 72

2^3 * 3^2

So to finish up we multiply 2 to the greatest power of two's found in the set, by the greater power of 3s in the set, by the greatest power of 5s in the set... (this could go on for however many unique primes are found in the factorization of the set. Also note, you may not write out a number to the first power, it's kind of redundant, it's just for demonstrative purposes.)

2^3 * 3^2 * 5^1 = 360