# Class 10 Solution: Find the smallest Perfect Square number which is divisible by 4, 9 and 10.

## Find the smallest Perfect Square number which is divisible by 4, 9 and 10. Answer: The smallest Perfect Square number which is divisible by 4, 9 and 10 is 900.

Solution: We need to find the smallest Perfect Square number which is divisible by 4, 9 and 10.

### Step – 1 : Find The LCM of 4, 9, 10

Why? Because, First of all, We need o find the lowest (smallest) common divisor of 4, 9 and 10 (or the number which is divisible by 4, 9 and 10, meaning is same).

• 4 = 2 × 2
• 9 = 3 × 3
• 10 = 2 × 5

Therefore, LCM(4, 9, 10) = 2 × 2 × 3 × 3 × 5 = 180

### Step – 2: Check whether 180 is a perfect square

We found that, the smallest common divisor of 4, 9 and 10 is 180.

so, if 180 is a perfect square, then 180 is the final answer. But, 180 is not a perfect square number. Because, the factors of 180 is 2 × 2 × 3 × 3 × 5, means, one pair of 2, one pair of 3 but only one single 5. to be perfect square, there should be pair of each factor.

### Step – 3: Increase 180 into a perfect square number.

Since, 180 is not a perfect square as there should be one more 5 in the factors.

So, to make 180 a perfect square, multiplying 180 by 5 we get,

180 × 5 = 900

Here, 900 (=30²) is obviously a perfect square number, which is the final answer.

Hope You have understood the solution. Please comment below if there is any more confusion and questions that you may have. Also, please comment if you have understood 100% clearly.

## Some More Questions Like “Find the smallest Perfect Square number which is divisible by 4, 9 and 10.”

### Two numbers are in the ratio 3:4. The LCM is 84. What is the greater number?

Solution: Given, Two numbers are in the ratio 3:4. The LCM is 84. We need to find the greater number.

#### Step – 1: Assume the GCD (or HCF) of the two number.

Let us assume that the HCF of the two number be x.

Then the two number will be 3x and 4x.

#### Step -2: Use The Formula

Now, use the formula:

Product of the two numbers = LCM × HCF

Or, 3x × 4x = 84 × x

Or, 12x = 84

Or, x = 7

#### Step -3: Find the larger or greater number now

Here, obviously, 4x will be the larger number.

So, larger number is = 4 × 7 = 28

(a) 18 hours

(b) 6 hours

(c) 12 hours

(d) 24 hours

### Few More Words For “Find the smallest Perfect Square number which is divisible by 4, 9 and 10.”

Actually this particular question is given in class 10 general mathematics book which is prepared by NCERT for state level class 10 examination and also for CBSE board examinations. This question is really very very important and a very common question for class 10 final board examinations.

This question is already taken in ASSAM HSLC  EXAMINATIONs, CBSE BOARD CLASS 10 exams, SSC GD, UPSC PSC, RRB SSC CHSL CGL MTS , Police Constable and more exams…

Hope You have Understood the Solution For

“Find the smallest Perfect Square number which is divisible by 4, 9 and 10.”

as well as “Two numbers are in the ratio 3:4. The LCM is 84. What is the greater number?”

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### Conclusions

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This question Find the smallest Perfect Square number which is divisible by 4, 9 and 10. … is a very common questions in most of the competative examinations from few years. The question is taken from class 10th science book. From NCERT provided CLASS 10 GENERAL Mathematics and from the content Physics, this particular question is taken and is very popular among us.

### Why the question Find the smallest Perfect Square number which is divisible by 4, 9 and 10 Important?

This question is from high school (HSLC) or 10th standard science. Which is also known as Elementary Mathematics Problem. And it is a common lesson for ongoing competitional exams and interviews.

Normally and most commonly it was taken in PSC, UPSC,  SSC , RRB or Railway NTPC and Group D, SSC CHSL, SSC MTS Multi Tasking Services, SSC CGL, SSC GD general duty, State level exams such as PNRD, SOIL CONSERVATION DEPARTMENT, SECRETARY ADMINISTRATIVE ASSISTANT JUNIOR AND SENIOR, POST OFFICE VACANCY etc etc.. So, carefully study it. Share it among your friends and discuss it. This is gonna help you a lot.

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