Question

If n is a natural number , then LCM of n , n 2 and n 3​

Answer 1

Answer:

72

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Given: Natural numbers $n, n^{2}, n^{3}$.

To Find: The LCM of $n, n^{2}, n^{3}$.

• We know, LCM is the smallest possible integer which is divisible by all the given numbers.
• For the numbers $n, n^{2}, n^{3}$, the factorization of each number is:

       ⇒ $n=n$

       ⇒ $n^{2} = n\times n$

       ⇒ $n^{3} = n\times n\times n$

• Here, we take $n$ common from each factorization and multiply each of them to obtain the LCM. So,

       ⇒ $LCM= n\times n\times n$

       ⇒ $LCM= n^{3}$

Therefore, LCM becomes $n^{3}$ for any natural numbers $n, n^{2}, n^{3}$.