Question

finding the lcm
find the lcm of the pair of expressions in the table.
drag the lcm to the appropriate expression.
lcm\texpression
$28a^2b^3$ \t$7a^2b^3$ and $4ab$
$2(x - 7)(x + 7)$ \t$x^2 - 49$ and $2x - 14$
$12(x - 3)(x + 3)$ \t
$(x + 2)(x + 8)(x - 7)$ \t$x^2 + x - 56$ and $x^2 - 5x - 14$
lcm

Explanation:

Step1: Factor $x^2 - 49$ and $2x -14$

$x^2 -49=(x-7)(x+7)$, $2x-14=2(x-7)$

Step2: Find LCM of Pair1

Take highest powers: $2(x-7)(x+7)$

Step3: Factor $7a^2b^3$ and $4ab$

$7a^2b^3=7a^2b^3$, $4ab=4ab$

Step4: Find LCM of Pair2

Take highest powers: $28a^2b^3$

Step5: Factor $x^2+x-56$ and $x^2-5x-14$

$x^2+x-56=(x+8)(x-7)$, $x^2-5x-14=(x-7)(x+2)$

Step6: Find LCM of Pair3

Take highest powers: $(x+8)(x-7)(x+2)$

Answer:

• Pair 1 ($x^2 - 49$ and $2x - 14$): $2(x - 7)(x + 7)$
• Pair 2 ($7a^2b^3$ and $4ab$): $28a^2b^3$
• Pair 3 ($x^2 + x - 56$ and $x^2 - 5x - 14$): $(x + 8)(x - 7)(x + 2)$