Question

find the smallest square number divisible by 6,8,15​

Answer 1

Answer: The smallest square number divisible by 6,8,15​ is 3600.

Step-by-step explanation:

• To find the smallest square number divisible by 6,8,15​, first, calculate the L.C.M.

• 6 = 2 x 3
• 8 = 2 x2 x2
• 15 = 3 x 5

L.C.M =  2  x 2 x 2 x 3 x  5

          =   120

As 2 , 3, 5 are not grouped in pair, multiply the L.C.M by 2 ,3 and 5

= 120 x 2 x 3 x 5

= 3600

3600 = (60)²

Thus, 3600 is the smallest square number divisible by 6, 8 ,15.

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Answer 2

Concept

LCM is the least multiple that is common to all of the given numbers.

Given

three numbers - 6, 8 and 15

Find

we need to find the smallest square number divisible by they 3 numbers given above.

Solution

Firstly, we will find the smallest number divisible by 6, 8 and 15. This will be given by their LCM.

The LCM of 8, 15 and 6 is 120.

However, 120 is not a square number. We need to find a multiple of 120 that is a square number.

120 can be written as

120 = 5 x 2 x 2 x 2 x 3

here, we can notice that 2, 3 and 5 are not grouped. To make 120 a perfect square we need to multiply it by 2 x 3 x 5

= 120 x 2 x 3 x 5

= 120 x 30

= 3600

Thus, the smallest square number that divides 6, 8 and 15 is 3600.

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