Find the least common multiple of the expressions. $5 y ^ { 2 } + 9 y - 2,15 y ^ { 2 } - 3 y$
A) $3 y ( y + 2 ) ( 5 y - 1 )$
B) $20 y ^ { 2 } + 6 y - 2$
C) $( 5 y - 1 ) ( y + 2 )$
D) $3 y ( 5 y - 1 )$
E) $75 y ^ { 2 } + 27 y - 2$

Question

Quizplus · Accepted Answer

The least common multiple (LCM) of two algebraic expressions is the smallest expression that both original expressions can divide into. To find the LCM, we factor each expression and then take the highest power of each factor that appears.The first expression, $5y^2 + 9y - 2$, can be factored into $(5y - 1)(y + 2)$.The second expression, $15y^2 - 3y$, can be factored out by taking $3y$ common, resulting in $3y(5y - 1)$.The LCM will include all unique factors from both expressions, taken to the highest power they appear in any one expression. Thus, the LCM is $3y(5y - 1)(y + 2)$, which matches choice A.

Find the Least Common Multiple of the Expressions 5y2+9y−2,15y2−3y5 y ^ { 2 } + 9 y - 2,15 y ^ { 2 } - 3 y5y2+9y−2,15y2−3y

Find the Least Common Multiple of the Expressions $5 y ^ { 2 } + 9 y - 2,15 y ^ { 2 } - 3 y$