Is 243 a perfect cube ? If not find the smallest natural number by which 243 must be multiplied so that the product is perfect cube ?
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Answered by
74
Solution:-
LCM of 243=
Here,we can see that 3 are in group of five.
For any number to be perfect cube its prime factor should be in group of three.
We have found 3 which is in group of five.
If we separate them we will find two group of three,one consisting 3 three times and other have three only two time.
So,in order to make a number a perfect cube ,its prime factor should be in group of three.
Hence,the number which should be multiplied by 243 to make it perfect cube is 3.
LCM of 243=
Here,we can see that 3 are in group of five.
For any number to be perfect cube its prime factor should be in group of three.
We have found 3 which is in group of five.
If we separate them we will find two group of three,one consisting 3 three times and other have three only two time.
So,in order to make a number a perfect cube ,its prime factor should be in group of three.
Hence,the number which should be multiplied by 243 to make it perfect cube is 3.
Answered by
24
Answer:
by prime factorization methods
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