Question

Let P is Prime number then what is L.C.M. of P Square, P, P Cube?

Answer 1

Given that p is a prime number, so p² and p³ cannot be divided by none other than powers of p.

i.e., p² can be divided by p⁰, p¹ and p² only.

And p³ can be divided by p⁰, p¹,  p² and p³ only.

Let me take the LCM.

$\begin{tabular}{c|l} p & p,\ p^2,\ p^3 \\ \cline{2-} p & 1,\ p,\ p^2 \\\cline{2-}& 1,\ 1,\ p \\\cline{2-}\end{tabular}$

Further simplification is not possible.

So the LCM is p · p · p = p³

No need to approach the method. If the largest among some numbers can be divided by others, then that one is the LCM of all.

Means, among p, p² and p³, p³ can be divided by both p and p². Hence p³ is the LCM of the three.

Answer 2

Answer:

Step-by-step explanation: