Question

Find the smallest perfect square divisible by 3, 4, 5, and 6

Answer 1

Step-by-step explanation:

Firstly, we will need to use prime factorisation.

3 and 5 are prime, while 4=22 and 6=2×3.

Therefore the lowest common multiple of the four numbers is 22×3×5=60.

Note that in the prime factorisation of perfect squares, the indices of the primes must be even. In the prime factorisation of 60, the indices of 3 and 5 are odd. Therefore we have to multiply 60 by 3 and 5. The answer, hence, is 60×3×5=900.

I hope it will helps you ARMY!!☺️

Answer 2

Take the LCM of 3, 4, 5 and 6.

We get LCM = 3 × 2 × 2 × 5 = 60.

         

DON'T TAKE 60! TAKE 3 × 2 × 2 × 5. IT'S THE PRIME FACTORIZED FORM OF 60.

     

∴ 60 = 2² × 3 × 5

To make 2² × 3 × 5 a perfect square, we need to multiply 3 and 5 to it, i.e., to multiply 3 × 5.

∵ (2² × 3 × 5) × (3 × 5)

⇒ 2² × 3 × 5 × 3 × 5

⇒ 2² × 3² × 5²

⇒ (2 × 3 × 5)²

⇒ 30²

⇒ 900

∴ 900 is the answer.

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