how do you determine a least common denominator?

Question

how do i determin the least common denominator between 5/6 and 2/9?

Answer 1

Given fractions are 5/6 and 2/9.

List the multiples of denominators.

Multiples of 6 are 6,12,18,24,30,36,42,48,54,60,...

Multiples of 9 are 9,18,27,36,45,54,63,72,..

Least common denominator of given fractions is 54.

Answer 2

Write the prime factorization of each denominator.

6 = 2 * 3 = 2¹ * 3¹

9 = 3 * 3 = 3²

Multiply highest power of each factor in the either number.

L.C.D = 2¹ * 3² 

           = 18