What is the least positive integer k for which 15k is the cube of a number?

Open in App

Solution

Prime factor of 15= $5 \times 3$
To make a perfect cube we make the pair of three in the prime factor.
$∴$ Prime factor is multiply by= $5 \times 5 \times 3 \times 3 = 225$

Suggest Corrections

Similar questions

Q. What is the least positive integer with which you have to multiply

243

to get a perfect cube?

Q. What is the smallest positive integer

K

such that

2000 \times 2001 \times K

is a perfect cube?

Q. The integer

k

for which the inequality

x^{2} - 2 (4 k - 1) x + 15 k^{2} - 2 k - 7 > 0

is valid for

x

, is

Q. The least positive integer

n

for which

{(\frac{1 + i}{1 - i})}^{n}

represents a real number is

The least positive integer k for which the value $k \times n^{2} (n^{2} - 1^{2}) (n^{2} - 2^{2}) . . . . (n^{2} - (n - 1)^{2})$ turns into a factorial of some positive integer is

Join BYJU'S Learning Program

What is the least positive integer k for which 15k is the cube of a number?

Prime factor of 15=5×3To make a perfect cube we make the pair of three in the prime factor.∴Prime factor is multiply by=5×5×3×3=225

Prime factor of 15= $5 \times 3$
To make a perfect cube we make the pair of three in the prime factor.
$∴$ Prime factor is multiply by= $5 \times 5 \times 3 \times 3 = 225$