Question

find the smallest square number which is exactly divisible by 4,5 and 8​

Answer 1

Answer:

400

Step-by-step explanation:

To find :

Smallest square which is exactly divisible by 4,5 and 8.

Procedure :

Firstly finding LCM of 4,5 and 8.

4 = 2²

5 = 5¹

8 = 2³

Hence, LCM of 4,5 and 8 is 2³ × 5¹.

In LCM, 2³ isn't a perfect square and neither is 5¹.

So, to convert them into perfect square,

2³ × 2 = 2⁴ = (2²)²

5¹ × 5 = 5² = (5)²

So Multiplying the LCM by 2 and 5 we get,

2⁴ × 5²

=> (2² × 5)²

=> (4 × 5)²

=> 20²

=> 400

Thanks !