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find the smallest square number which is exactly divisible by 10,12,18,24
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Most Upvoted Answer
find the smallest square number which is exactly divisible by 10,12,18...
The small square number which is divisible by 10,12,18,24 will be 2.
So the answer is 2.
So the answer is 2.
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find the smallest square number which is exactly divisible by 10,12,18...
Introduction:
To find the smallest square number that is exactly divisible by 10, 12, 18, and 24, we need to first find the prime factorizations of these numbers. Then, we can determine the least common multiple (LCM) of these prime factorizations. Finally, we will square the LCM to find the smallest square number divisible by all the given numbers.
Step 1: Prime Factorization:
Let's find the prime factorizations of the given numbers:
10 = 2 × 5
12 = 2^2 × 3
18 = 2 × 3^2
24 = 2^3 × 3
Step 2: LCM of Prime Factorizations:
Next, we need to find the LCM of the prime factorizations. To do this, we take the highest power of each prime factor that appears in any of the factorizations.
The LCM of the prime factorizations is:
LCM = 2^3 × 3^2 × 5 = 8 × 9 × 5 = 360
Step 3: Square the LCM:
Finally, to find the smallest square number that is divisible by all the given numbers, we square the LCM.
Smallest square number = (LCM)^2 = 360^2 = 129,600
Conclusion:
The smallest square number that is exactly divisible by 10, 12, 18, and 24 is 129,600.
To find the smallest square number that is exactly divisible by 10, 12, 18, and 24, we need to first find the prime factorizations of these numbers. Then, we can determine the least common multiple (LCM) of these prime factorizations. Finally, we will square the LCM to find the smallest square number divisible by all the given numbers.
Step 1: Prime Factorization:
Let's find the prime factorizations of the given numbers:
10 = 2 × 5
12 = 2^2 × 3
18 = 2 × 3^2
24 = 2^3 × 3
Step 2: LCM of Prime Factorizations:
Next, we need to find the LCM of the prime factorizations. To do this, we take the highest power of each prime factor that appears in any of the factorizations.
The LCM of the prime factorizations is:
LCM = 2^3 × 3^2 × 5 = 8 × 9 × 5 = 360
Step 3: Square the LCM:
Finally, to find the smallest square number that is divisible by all the given numbers, we square the LCM.
Smallest square number = (LCM)^2 = 360^2 = 129,600
Conclusion:
The smallest square number that is exactly divisible by 10, 12, 18, and 24 is 129,600.
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find the smallest square number which is exactly divisible by 10,12,18,24 Related: Finding Square Root By Prime Factorisation: Part 2?
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find the smallest square number which is exactly divisible by 10,12,18,24 Related: Finding Square Root By Prime Factorisation: Part 2? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about find the smallest square number which is exactly divisible by 10,12,18,24 Related: Finding Square Root By Prime Factorisation: Part 2? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for find the smallest square number which is exactly divisible by 10,12,18,24 Related: Finding Square Root By Prime Factorisation: Part 2?.
find the smallest square number which is exactly divisible by 10,12,18,24 Related: Finding Square Root By Prime Factorisation: Part 2? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about find the smallest square number which is exactly divisible by 10,12,18,24 Related: Finding Square Root By Prime Factorisation: Part 2? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for find the smallest square number which is exactly divisible by 10,12,18,24 Related: Finding Square Root By Prime Factorisation: Part 2?.
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