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Find the smallest square number which is divisible by each of the numbers 6, 9 and 15.?
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Find the smallest square number which is divisible by each of the numb...
Finding the Smallest Square Number Divisible by 6, 9, and 15
To determine the smallest square number that is divisible by 6, 9, and 15, we begin by identifying the least common multiple (LCM) of these numbers.
Step 1: Prime Factorization
- For 6: 2 × 3
- For 9: 3²
- For 15: 3 × 5
Step 2: Identify the LCM
- Take the highest power of each prime factor:
- 2 (from 6) → 2¹
- 3 (from 9) → 3²
- 5 (from 15) → 5¹
- Thus, the LCM is:
- LCM = 2¹ × 3² × 5¹ = 2 × 9 × 5 = 90
Step 3: Finding the Smallest Square Number
To find a square number, all prime factors in its prime factorization must have even powers.
- The prime factorization of 90: 2¹ × 3² × 5¹
- To make the powers even, we adjust:
- For 2: Increase from 1 to 2 (add 1)
- For 3: Already 2 (no change needed)
- For 5: Increase from 1 to 2 (add 1)
This gives us the modified prime factorization:
- New LCM = 2² × 3² × 5²
Step 4: Calculate the Smallest Square Number
Now calculate:
- 2² = 4
- 3² = 9
- 5² = 25
Now multiply these values:
- 4 × 9 × 25 = 900
Final Answer
The smallest square number that is divisible by 6, 9, and 15 is 900.
To determine the smallest square number that is divisible by 6, 9, and 15, we begin by identifying the least common multiple (LCM) of these numbers.
Step 1: Prime Factorization
- For 6: 2 × 3
- For 9: 3²
- For 15: 3 × 5
Step 2: Identify the LCM
- Take the highest power of each prime factor:
- 2 (from 6) → 2¹
- 3 (from 9) → 3²
- 5 (from 15) → 5¹
- Thus, the LCM is:
- LCM = 2¹ × 3² × 5¹ = 2 × 9 × 5 = 90
Step 3: Finding the Smallest Square Number
To find a square number, all prime factors in its prime factorization must have even powers.
- The prime factorization of 90: 2¹ × 3² × 5¹
- To make the powers even, we adjust:
- For 2: Increase from 1 to 2 (add 1)
- For 3: Already 2 (no change needed)
- For 5: Increase from 1 to 2 (add 1)
This gives us the modified prime factorization:
- New LCM = 2² × 3² × 5²
Step 4: Calculate the Smallest Square Number
Now calculate:
- 2² = 4
- 3² = 9
- 5² = 25
Now multiply these values:
- 4 × 9 × 25 = 900
Final Answer
The smallest square number that is divisible by 6, 9, and 15 is 900.
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Find the smallest square number which is divisible by each of the numbers 6, 9 and 15.?
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Find the smallest square number which is divisible by each of the numbers 6, 9 and 15.? 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 divisible by each of the numbers 6, 9 and 15.? 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 divisible by each of the numbers 6, 9 and 15.?.
Find the smallest square number which is divisible by each of the numbers 6, 9 and 15.? 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 divisible by each of the numbers 6, 9 and 15.? 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 divisible by each of the numbers 6, 9 and 15.?.
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