What is the smallest natural number by which 243 must be multiplied so that the product is a perfect cube?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 3
A number is a perfect cube when, in its prime factorisation, every prime appears a multiple of 3 times. Multiply by the fewest primes needed to reach the next multiple of 3.
\(243=3\times3\times3\times3\times3=3^{5}\)
The next multiple of 3 after the power 5 is 6, so one more 3 is needed
\(243\times3=729=3^{6}=9^{3}\), a perfect cube