Question

Find the smallest square number that is divisible by each of the numbers 4,9 and 10

Answer 1

Let us find LCM of 4, 9 and 10
4 = 2 x 2
9 = 3 x 3
10 = 5 x 2
So, LCM = 2 2 x 3 2 x 5 = 180
Now the LCM gives us a clue that if 180 is multiplied by 5 then it will become a perfect square.
The Required number = 180 x 5 = 900

Answer 2

The smallest square number that is divisible by each of the numbers 4,9 and 10 is 900

Solution:

We have to find the smallest square number that is divisible by each of the numbers 4,9 and 10

First we have to calculate  L.C.M of 4 , 9 and 10

The prime factors of 4 = $2 \times 2$

The prime factors of 9 = $3 \times 3$

The prime factors of 10 = $2 \times 5$

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

2, 2, 3, 3, 5

Multiply these factors together to find the LCM.

$LCM = 2 \times 2 \times 3 \times 3 \times 5$

To make it a perfect square, we have to multiply by "5"

$2 \times 2 \times 3 \times 3 \times 5 \times 5$

$4 \times 9 \times 25 =900$

Which is the smallest square number divisible by 4,9 and 10

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