lcd help please

Question

Least common denominator of a² b,ab² 

Answer 1

The least common denominator, lcd, is used when dealing with fractions and because neither of these are fractions the answer for lcd would be 1. However, the least common multiple, lcm, is the "least number that is a common multiple of two or more numbers".

First, find the prime factors of each number (polynomial)

                            a²b: a X a X b

                            ab²: a X b X b

Now, use each prime factor the greatest number of times that appears in any factorization

                            a X a X b ---> a² X b--->2 a's and 1 b

                            a X b X b ---> a X b²--->1 a and 2 b's

Therefore, the lcm is a² X b², or a²b².