Answer :

jacob193

Answer:

[tex]8100[/tex], which is the square of [tex]90[/tex].

Step-by-step explanation:

Factor the three divisors into prime numbers:

  • [tex]5[/tex] is a prime number itself.
  • [tex]6 = 2\times 3[/tex].
  • [tex]27 = 3^3[/tex].

Any number divisible by these three divisors should include the following factors:

  • [tex]2[/tex],
  • [tex]3^3[/tex], and
  • [tex]5[/tex].

Note that all these three prime factors have an odd power ([tex]1[/tex], [tex]3[/tex], and [tex]1[/tex], respectively)

  • [tex]2[/tex] becomes [tex]2^2[/tex] (add [tex]1[/tex] to the initial power of [tex]1[/tex] to obtain [tex]2[/tex].)
  • [tex]3^3[/tex] becomes [tex]3^4[/tex].
  • [tex]5[/tex] becomes [tex]5^2[/tex].

The product of these three factors would be:

[tex]2^2 \times 3^4 \times 5^2 = 8100[/tex].

Indeed, [tex]8100[/tex] is divisible by all these three divisors. At the same time, because all the powers of its prime factors are even,

[tex]8100 = (2 \times 3^2 \times 5)^2 = 90^2[/tex].

devishri1977

Answer:

8100 is the smallest perfect square divisible by 5,6 and 27

Step-by-step explanation:

5 = 5 * 1

6 = 2 * 3

27 = 3 * 3 *3

5 * 6 * 27 = 2 * 3 * 3 * 3 * 3 * 5

Factors of perfect square will be perfect squares

To make this a perfect, multiply by 5 * 2

Perfect square = 5 * 6 * 27 * 5 * 2

                        = 8100

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