Cube n Fourth power??

[adi_800]

What is the smallest natural number that is a cube of a natural number and fourth power of a different natural number?

SPOILER: OA is 4096

[Fiver]

Originally Posted by adi_800

What is the smallest natural number that is a cube of a natural number and fourth power of a different natural number?

SPOILER: OA is 4096

Since the no. has to be the 3rd power as well as the 4th power of 2 diff nos and still in the process has to be the smallest possible natural no, its best to start with the smallest possible natural no. rasied to the LCM of 3 & 4 i.e.12.
The smallest natural no. is 1, but 1 is irrelevant here since the cube root and the 4th root of 1 is the same.
Hence the answer is 2^12, the cube root of which is 2^4 and the 4th root of which is 2^3; hence diff nos.

[finsisher]

well done Fiver

[Fiver]

Originally Posted by finsisher

well done Fiver

Thanks champ