Question

The LCM of a³ + 2a² and 2a³ + 5a²

• A. $a^2$ (2a + 5)
• B. $a^2$ (a + 2)
• C. $a^2$ (a + 2) (2a + 5)
• D. (a + 2) (2a + 5)

Answer 1

The correct option is C

$a^2$ (a + 2) (2a + 5)

To find the LCM of a³ + 2a² and 2a³ + 5a² we will write them in the following form,

a³ + 2a² = a$\times$a$\times$a + 2$\times$a$\times$a

2a³ + 5$a^2$ = 2$\times$a$\times$a$\times$a + 5$\times$a$\times$a

So, the only common terms in this is $a^2$ i.e. HCF = $a^2$

Then, LCM = HCF $\times$ uncommon terms = $a^2$ (a + 2) (2a + 5) (Answer)