Question

find the smallest square number which is divisible by each of the numbers 8 ,12 ,15 ,20 with explainataion.
thank you​

Answer 1

Answer:

5 is the smallest sqare no.

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Answer 2

Answer:

3600

Step-by-step explanation:

First find LCM of 8,12,15 and 20 because we should find a number which is divisible of all these numbers and so, it should have a common factor.

LCM:

8 = 2³

12 = 2² × 3

15 = 3 × 5

20 = 2² × 5

LCM = 2³ × 3 × 5

Now, notice that for square number, the exponents will always be even.

Like, for example, 2 × 2 = 2² = 4 is a square number.

So, we will add 1 to all the odd exponents.

2³ × 2 = 2⁴

3 × 3 = 3²

5 × 5 = 5²

Now multiply the products.

2⁴ × 3² × 5² = 3600

Hope it helps you:)