Question

1.find the smallest square number that is divisible by each of the numbers 5,10 and 25.
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Answer 1

Step-by-step explanation:

2 number is smallest square number is dividable of 5,10and 25

Answer 2

Answer:

The smallest square number which is divisible by all the given three numbers 5, 10 and 25 is 100.

Step-by-step explanation:

Given,  

Two things we need to consider,

1. The number should be divided by 5, 10 and 25

2. It should be a square number.

Considering first one,  

Find out the LCM of 5, 10 and 25

We get.

$5 = 5\\\\10 = 5 \times2\\\\25 = 5\times5$

Thus, the LCM $=5\times5\times2=5^2\times2^1$

In order to get a perfect square, the powers must be even so we are now multiplying by 2 to make the power of 2 as an even one.

Thus, the LCM becomes  

$=5^2\times2\times2\\\\=5^2\times2^2\\\\=25\times4\\\\=100$

Thus, 100 is a square number and it is divisible by all the three numbers i.e., 5, 10 and 25.

Thus, the number is 100.