Question

The LCM of $a^k,a^{k+3},a^{k+5}$ where $kϵN$ is

• A. $a^{k+9}$
• B. $a^k$
• C. $a^{k+6}$
• D. $a^{k+5}$

Answer 1

Answer: (D)

$a^{k+5}$

LCM of $a^k,a^k+5,a^k+5$

Using Prime Factorization Method

$a^k=a\times a\times a.........ktimes$

$a^{k+3}=a\times a\times a.........k+3times$

$a^{k+5}=a\times a\times a.........k+5times$

Now we will select the highest power of each prime factor

So,LCM of $(a^k,a^k+3,a^k+5)=a^{k+5}$

Correct Answer is $D$