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What is the least perfect square which is divisible by 2, 4 and 6?
- a)36
- b)64
- c)16
- d)18
Correct answer is option 'A'. Can you explain this answer?
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What is the least perfect square which is divisible by 2, 4 and 6?a)36...
LCM of 2,4,6= 2×1×2×3=12
Least perfect square which is a multiple of 12 is 36.
Least perfect square which is a multiple of 12 is 36.
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What is the least perfect square which is divisible by 2, 4 and 6?a)36...
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What is the least perfect square which is divisible by 2, 4 and 6?a)36...
To find the least perfect square that is divisible by 2, 4, and 6, we need to consider the prime factors of these numbers.
Prime Factors of 2: 2
Prime Factors of 4: 2^2
Prime Factors of 6: 2 * 3
To find the least perfect square that is divisible by all three numbers, we need to take the highest power of each prime factor that appears in any of the three numbers.
Taking the highest power of 2, we have 2^2 = 4.
Taking the highest power of 3, we have 3^1 = 3.
Therefore, the least perfect square that is divisible by 2, 4, and 6 is 4 * 3 = 12.
However, 12 is not a perfect square. To find the least perfect square, we need to find the square of 12, which is 12^2 = 144.
Therefore, the least perfect square that is divisible by 2, 4, and 6 is 144.
Now let's check the given options:
a) 36: 36 is divisible by 2 and 6, but not by 4.
b) 64: 64 is divisible by 2 and 4, but not by 6.
c) 16: 16 is divisible by 2 and 4, but not by 6.
d) 18: 18 is divisible by 2 and 6, but not by 4.
None of the given options are divisible by all three numbers.
Therefore, the correct answer is option 'A' (36).
Prime Factors of 2: 2
Prime Factors of 4: 2^2
Prime Factors of 6: 2 * 3
To find the least perfect square that is divisible by all three numbers, we need to take the highest power of each prime factor that appears in any of the three numbers.
Taking the highest power of 2, we have 2^2 = 4.
Taking the highest power of 3, we have 3^1 = 3.
Therefore, the least perfect square that is divisible by 2, 4, and 6 is 4 * 3 = 12.
However, 12 is not a perfect square. To find the least perfect square, we need to find the square of 12, which is 12^2 = 144.
Therefore, the least perfect square that is divisible by 2, 4, and 6 is 144.
Now let's check the given options:
a) 36: 36 is divisible by 2 and 6, but not by 4.
b) 64: 64 is divisible by 2 and 4, but not by 6.
c) 16: 16 is divisible by 2 and 4, but not by 6.
d) 18: 18 is divisible by 2 and 6, but not by 4.
None of the given options are divisible by all three numbers.
Therefore, the correct answer is option 'A' (36).
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What is the least perfect square which is divisible by 2, 4 and 6?a)36b)64c)16d)18Correct answer is option 'A'. Can you explain this answer?
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