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

ANSWER

The correct answer is D.

EXPLANATION

If we express the monomial,

$18 {x}^{2} y$

as product of primes, we obtain:

$2 \times {3}^{2} \times {x}^{2}y$

If we express the monomial

$27x {y}^{3}$

as product of primes we obtain:

$= {3}^{3} \times x {y}^{3}$

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

The LCM is

$= 2 \times {3}^{3} \times {x}^{2} {y}^{3}$

$=54 {x}^{2} {y}^{3}$

Therefore the correct answer is D.

Answer 2

Answer:

The correct answer is option D.

18x2y, 27xy3

Step-by-step 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