Question

find the smallest square
number which is exactly
divisible by 8, 2, 20​

Answer 1

Answer:

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Step-by-step explanation:

The first number divisible by 8, 2 and 20 will be their LCM i.e 40.

But on Factorising 40 we find that it's factors are not in pairs, whereas pairing is the first rule of finding a square or a square root of any number.

Factors of 40 are 2^3 × 5^1.

Here we see that each prime number needs one more power to become a pair so we increase each of their exponential powers by one and get 2^4 × 5^2 which is equal to 400.

And therefore we conclude that the smallest square number divisible by 8, 2 and 20 is 400, which is the square of 20.

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If ur question is find the smallest square number which is divisible by 8, 15, and 20?

The first number divisible by 8, 15 and 20 will be their LCM i.e 120.

But on Factorising 120 we find that it's factors are not in pairs, whereas pairing is the first rule of finding a square or a square root of any number.

Factors of 120 are 2^3 × 3^1 × 5^1.

Here we see that each prime number needs one more power to become a pair so we increase each of their exponential powers by one and get 2^4 × 3^2 × 5^2 which is equal to 3600.

And therefore we conclude that the smallest square number divisible by 8, 15 and 20 is 3600, which is the square of 60.