Question

Which pair of monomials has the least common multiple (LCM) of 54x2y3?

A) 2xy, 27xy2
B) 3x2y3, 18x2y3
C) 6x2, 9y3
D) 18x2y, 27xy3

Answer 1

The correct answer is option D.

18x2y, 27xy3

Explanation:

To find the LCM

A).To find the Lcm of (2xy, 27xy2)

LCM((2xy, 27xy2) = 54xy^2

B).To find the Lcm of (3x2y3, 18x2y3)

LCM(3x2y3, 18x2y3) = 18x^2y^4

C). To find the Lcm of (6x2, 9y3)

LCM(6x2, 9y3) = 18y^2y^

D). To find the Lcm of (18x2y, 27xy3)

LCM(18x2y, 27xy3) = 54x^2y^3

Therefore the correct answer is option D

18x2y, 27xy3

Answer 2

The correct answer is D.

EXPLANATION

If we express the monomial,

`18 {x}^(2) y`

as product of primes, we obtain:

`2 * {3}^(2) * {x}^(2)y`

If we express the monomial

`27x {y}^(3)`

as product of primes we obtain:

`= {3}^(3) * x {y}^(3)`

The least common multiple of these two binomials is the product of the highest powers of the common factors.

The LCM is

`= 2 * {3}^(3) * {x}^(2) {y}^(3)`

`=54 {x}^(2) {y}^(3)`

Therefore the correct answer is D.