What is the smallest positive integer k such that the product is a perfect square?

So we can safely conclude that 7 is the least integer k such that 1575k is a perfect square.

How do you solve the smallest positive integer k?

1. 2520=2^3*3^2*5*7.
2. And we need to remove the least number from them to make 2520 be a perfect square.
3. It means we need to make all the exponential to be even: 2^2*3^2=36.
4. So the smallest k is 2520/36=2*5*7=70.

How do you find the least perfect cube?

⇒ The least perfect cube is 216 divisible by 12.

How do you find the smallest integer of a perfect square?

L.C.M. of 8, 15 and 20 is 120. Here, prime factors 2, 3 and 5 have no pair. Therefore 120 must be multiplied by 2 x 3 x 5 to make it a perfect square. Hence, the smallest square number which is divisible by 8, 15 and 20 is 3600.

What is the smallest integer k such that ✓ n is in O N K?

and since the exponents can’t be negative (if k is to be an integer), then to make k as small as possible, we’ll need m1=2 and m2,m3=1, whence it follows that k=22⋅32⋅55.

What’s the smallest perfect square?

16 and 18 are the smallest and the largest 2-digit perfect squares.

What is a perfect cube?

The perfect cube is the result of multiplying the same integer three times. Multiplying the number 4 three times, for example, yields 64. As a result, the number 64 is a perfect cube. If a number can be broken down into a product of the same three numbers, it is said to be a perfect cube. …

What is the least perfect cube divisible by 2 3 4 and 6?

36 is divisible by 2,3,4&6. Ans.

What is the smallest possible value of K?

Based on the above prime factorization, each of the two terms will have to include one 3, one 5 and one 7…. Thus, K the smallest possible value of K is 7. swerve wrote: What is the smallest integer K such that the product of 1575 x K is a perfect square?

Can a perfect cube have a negative K?

So no matter how large of a negative k you pick, there will always be a more negative k (smaller k) that will produce a negative perfect cube. I will assume that k is a positive integer. If zero is allowed for k, then 0 is the smallest integer, for k (cube root of 0 = 0).

What is the perfect cube of 2000x2001k?

2000×2001K is a perfect cube. For a given number to be a perfect cube, power of all prime factors should be a multiple of 3. Thanks for A2A. There maybe many ways to do this, but only one comes to mind: factorizing (not a word?). 667 is a prime number. K= 16,016,004.

What is the minimum value of K for 729?

If it is acceptable to accept values of k that are rational numbers but not integers the minimum value of k is 1.35 which when multiplied to 2² × 3³ × 5 * 1.35 gives a perfect square of 729 because 729 = 27 * 27. , Took 5 college math courses. Given that 150k is a perfect square, what is the smallest possible integer value of k?