What is the smallest integer k such that 540k is a cube number?

Answer 1

You can factor 540 into prime factors. Then, for each prime factor that doesn't appear 3, 6, 9, ... times, add additional factors to complete a multiple of 3. These factors will make up the number "k".

Answer 2

Oh, dude, so like, the smallest integer k such that 540k is a cube number is 125. Because, you know, 540 times 125 equals 67500, which is a cube number. It's like math magic, but with cubes instead of rabbits.

Answer 3

To find the smallest integer k such that 540k is a cube number, we need to factorize 540 into its prime factors: 2^2 * 3^3 * 5. To make 540k a cube number, we need to balance the powers of each prime factor such that they are all multiples of 3. Therefore, we need to find the smallest integer k such that the powers of 2, 3, and 5 in 540k are all multiples of 3. This means k = 3^2 * 5^2 = 225.

Answer 4

Oh, what a happy little math problem! To find the smallest integer k such that 540k is a cube number, we need to break down 540 into its prime factors: 2^2 * 3^3 * 5. To make 540k a cube number, we need to balance the powers of each prime factor, so k must be 2 * 3^2 * 5^2 = 450. So, the smallest integer k that makes 540k a cube number is 450.

Answer 5

50