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Find the least square number (perfect square) which is exactly divisible by each of the numbers 6, 9, 12
a)36
b)65
c)81
d)49
Correct answer is option 'A'. Can you explain this answer?
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Find the least square number (perfect square) which is exactly divisib...
Least Square number divisible by 6, 9, and 12
To find the least square number that is exactly divisible by 6, 9, and 12, we need to find the least common multiple (LCM) of these numbers. Since the LCM of 6, 9, and 12 is the smallest number that is a multiple of all three numbers, it will be the least square number that is divisible by 6, 9, and 12.
Finding the LCM
- The prime factorization of 6 is 2 * 3
- The prime factorization of 9 is 3 * 3
- The prime factorization of 12 is 2 * 2 * 3
To find the LCM, we take the highest power of each prime factor that appears in any of the numbers. So, the LCM of 6, 9, and 12 is 2^2 * 3^2 = 36.
Verification
To verify that 36 is a perfect square and is divisible by 6, 9, and 12:
- 36 is a perfect square (6^2)
- 36 is divisible by 6 (36/6 = 6), 9 (36/9 = 4), and 12 (36/12 = 3)
Therefore, the least square number that is exactly divisible by each of the numbers 6, 9, and 12 is 36. So, the correct answer is option A.
To find the least square number that is exactly divisible by 6, 9, and 12, we need to find the least common multiple (LCM) of these numbers. Since the LCM of 6, 9, and 12 is the smallest number that is a multiple of all three numbers, it will be the least square number that is divisible by 6, 9, and 12.
Finding the LCM
- The prime factorization of 6 is 2 * 3
- The prime factorization of 9 is 3 * 3
- The prime factorization of 12 is 2 * 2 * 3
To find the LCM, we take the highest power of each prime factor that appears in any of the numbers. So, the LCM of 6, 9, and 12 is 2^2 * 3^2 = 36.
Verification
To verify that 36 is a perfect square and is divisible by 6, 9, and 12:
- 36 is a perfect square (6^2)
- 36 is divisible by 6 (36/6 = 6), 9 (36/9 = 4), and 12 (36/12 = 3)
Therefore, the least square number that is exactly divisible by each of the numbers 6, 9, and 12 is 36. So, the correct answer is option A.
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Community Answer
Find the least square number (perfect square) which is exactly divisib...
It should be 36, 24 is not a perfect square!
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Find the least square number (perfect square) which is exactly divisible by each of the numbers 6, 9, 12a)36b)65c)81d)49Correct answer is option 'A'. Can you explain this answer?
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