Question

If $a=2^3\times 3$, $b=2\times 3\times 5$, $c=3^n\times 5$ and LCM ($a,b,c$) $=2^3\times 3^2\times 5$, then $n=$ ? (Here, $n$ is a natural number)

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is B 2

Given: $a=2^3\times 3$
$b=2\times 3\times 5$
$c=3^n\times 5$
LCM ($a,b,c$)$=2^3\times 3^2\times 5$ ... (1)
Since, to find LCM we need to take the prime factors with their highest degree:
$\therefore$ LCM will be $2^3\times 3^n\times 5$ ... (2) $(n\ge 1)$
On comparing we get,
$n=2$