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If p is a prime number then LCM of p , p2, p3 is :

A ) p

B ) p3

C ) p2

D ) p6

 Option 3. P3

p=p

p2=p*p

p3=p*p*p

therefore. LCM is p3

 

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If p is a prime number then find LCM of p, p²and p³
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I m not understanding how it would be p^3
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This can be solved by the simple logic given in ncert book.
LCM = Product of the greatest power of each prime factor involved in the numbers.
Here, the greatest power is p?.
Hence, the answer.

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Step I: Resolve each given number into its prime factors and express the factors obtained in exponent form. Step I: Find the product of the highest powers of all the factors that occur in any of the given numbers. Step III: The product obtained in Step II is the required least common multiple (L.C.M) Hence when we make prime factors of p,p^2,p^3 we are able to see that p^3 So that p^3is a has highest power
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yess
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Etuhfffuu
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if n is natural number then exactly one of numbers n
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IF p is a prime number then LCM of P, P2 and P3 is- (a) P (b) P3 (c) P2 (d) P6
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Given:

p is prime number.

To find:

the lcm of p, p2,p3.

Solution:

1) If p is a prime number it is very clear that the LCM of p, p² and p³ is p³

2) Let us take the example to prove the above statement .

3) Let p = 3, p² = 9 and p³ = 27.

4) LCM(3,9,27) = 27

Hence, the LCM of p, p² and p³ is p³.

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