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

Question

Answer

Answer

Finding the Smallest Square Number Divisible by 4, 9, and 10

Step 1: Find the Prime Factors

To find the smallest square number divisible by 4, 9, and 10, we need to first find the prime factors of each number:

- 4 = 2 x 2
- 9 = 3 x 3
- 10 = 2 x 5

Step 2: Identify the Common Factors

Next, we need to identify the common factors among the prime factors:

- 2 x 2
- 3 x 3
- 2 x 5

Step 3: Multiply the Common Factors

To find the smallest square number that is divisible by all three numbers, we need to multiply the common factors:

2 x 2 x 3 x 3 x 2 x 5 = 180

Step 4: Find the Smallest Square Number

The smallest square number that is divisible by all three numbers is the square of the product of the common factors:

(2 x 2 x 3 x 3 x 2 x 5)^2 = 32400

Therefore, the smallest square number that is divisible by 4, 9, and 10 is 32400.

Answer

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

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Answer

FIND THE SMALLEST NUMBER THAT IS DIVISIBLE BY EACH OF THE NUMBER 4,9AND10

Answer

900

Answer

424474

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