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Which is the smallest square number that is divisible by each of the number 4,9 and10?
- a)900
- b)810
- c)800
- d)920
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Which is the smallest square number that is divisible by each of the n...
L.C.M. of 4, 9 and 10 is 180.
Prime factors of 180 =2*2*3*3*5
Here, prime factor 5 has no pair. Therefore 180 must be multiplied by 5 to make it a perfect square.
180*5 =900
Hence, the smallest square number which is divisible by 4, 9 and 10 is 900.
This question is part of UPSC exam. View all Quant courses
Most Upvoted Answer
Which is the smallest square number that is divisible by each of the n...
The smallest square number that is divisible by each of the numbers 4, 9, and 10 can be found by finding the least common multiple (LCM) of these three numbers.
To find the LCM, we need to find the prime factorization of each number and take the highest power of each prime factor.
Prime factorization of 4:
4 = 2^2
Prime factorization of 9:
9 = 3^2
Prime factorization of 10:
10 = 2 * 5
Now, we take the highest power of each prime factor:
2^2 * 3^2 * 5 = 900
Therefore, the smallest square number that is divisible by each of the numbers 4, 9, and 10 is 900.
Explain step by step:
1. Find the prime factorization of each number:
- Prime factorization of 4: 4 = 2^2
- Prime factorization of 9: 9 = 3^2
- Prime factorization of 10: 10 = 2 * 5
2. Take the highest power of each prime factor:
- Highest power of 2: 2^2
- Highest power of 3: 3^2
- Highest power of 5: 5^1 (as there is no other power of 5)
3. Multiply the highest powers of each prime factor:
- 2^2 * 3^2 * 5 = 900
4. Therefore, the smallest square number that is divisible by each of the numbers 4, 9, and 10 is 900.
To find the LCM, we need to find the prime factorization of each number and take the highest power of each prime factor.
Prime factorization of 4:
4 = 2^2
Prime factorization of 9:
9 = 3^2
Prime factorization of 10:
10 = 2 * 5
Now, we take the highest power of each prime factor:
2^2 * 3^2 * 5 = 900
Therefore, the smallest square number that is divisible by each of the numbers 4, 9, and 10 is 900.
Explain step by step:
1. Find the prime factorization of each number:
- Prime factorization of 4: 4 = 2^2
- Prime factorization of 9: 9 = 3^2
- Prime factorization of 10: 10 = 2 * 5
2. Take the highest power of each prime factor:
- Highest power of 2: 2^2
- Highest power of 3: 3^2
- Highest power of 5: 5^1 (as there is no other power of 5)
3. Multiply the highest powers of each prime factor:
- 2^2 * 3^2 * 5 = 900
4. Therefore, the smallest square number that is divisible by each of the numbers 4, 9, and 10 is 900.
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Which is the smallest square number that is divisible by each of the n...
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Which is the smallest square number that is divisible by each of the number 4,9 and10?a)900b)810c)800 d)920Correct answer is option 'A'. Can you explain this answer?
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