Im stuck on this question:
What is the smallest positive integer that is divisible by the factor 2,3 and 5 and which is also square and a cube. Prove that this is the smallest such integer.
how would i start this?
thanks
In the prime factorization of a perfect square, the exponent of each factor must divide 2. Similarly, for a perfect cube, the exponent of each factor must divide 3. So, your answer is going to be $\displaystyle (2\cdot3\cdot5)^6$.
This is how I would start the process of answering the problem. The language of the formal proof is the next step.