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What is the smallest positive perfect square that is divisible by the four smallest numbers?
The four smallest positive integers are 1, 2, 3, and 4. To find the smallest positive perfect square divisible by these numbers, we first determine their least common multiple (LCM). The LCM of 1, 2, 3, and 4 is 12. The smallest perfect square greater than or equal to 12 is 36, which is (6^2). Thus, the smallest positive perfect square that is divisible by 1, 2, 3, and 4 is 36.
What is the smallest positive perfect square that is divisible by 2 3 5 7?
To find the smallest positive perfect square that is divisible by 2, 3, 5, and 7, we first determine the least common multiple (LCM) of these numbers. The LCM is (2^1 \times 3^1 \times 5^1 \times 7^1 = 210). For a number to be a perfect square, all prime factors must have even exponents. Thus, we square the LCM, yielding (210^2 = 44100). Therefore, the smallest positive perfect square that is divisible by 2, 3, 5, and 7 is 44100.
What is the smallest positive integer n such that 2n is a perfect square 3n is a perfect cube and 4n is a perfect fourth?
To find the smallest positive integer ( n ) such that ( 2n ) is a perfect square, ( 3n ) is a perfect cube, and ( 4n ) is a perfect fourth, we analyze the conditions for each case using prime factorization. Let ( n = 2^a \cdot 3^b \cdot k ), where ( k ) is coprime to 2 and 3. For ( 2n ) to be a perfect square, ( a+1 ) must be even and ( b ) must be even. For ( 3n ) to be a perfect cube, ( a ) must be divisible by 3 and ( b+1 ) must be divisible by 3. For ( 4n ) to be a perfect fourth, ( a+2 ) must be divisible by 4 and ( b ) must be divisible by 4. By solving these conditions simultaneously, the smallest ( n ) that meets all conditions is ( n = 108 ).
What number is a perfect square and the sum of 2 perfect squares?
25 = 9 + 16 There are many more sets like these. This one has the smallest numbers.
What are the characteristics of a perfect square?
divisible by 2
What is the smallest positive perfect square that is divisible by the four smallest prime numbers?
(3x5x7x11)2 =1334025
What is the smallest positive perfect square that is divisible by the four smallest numbers?
The four smallest positive integers are 1, 2, 3, and 4. To find the smallest positive perfect square divisible by these numbers, we first determine their least common multiple (LCM). The LCM of 1, 2, 3, and 4 is 12. The smallest perfect square greater than or equal to 12 is 36, which is (6^2). Thus, the smallest positive perfect square that is divisible by 1, 2, 3, and 4 is 36.
What is the smallest perfect square that is divisible by the four smallest primes?
44,100
Smallest perfect square divisible by 7?
It is 49.
What is the smallest negative perfect square that is divisible by the four smallest prime numbers?
Perfect squares are positive. A smallest negative number doesn't exist. The four smallest prime numbers are 2, 3, 5 and 7. The smallest perfect square would have to be 2^2 x 3^2 x 5^2 x 7^2 or 44,100
What is the smallest positive perfect square that is divisible by 2 3 5 7?
To find the smallest positive perfect square that is divisible by 2, 3, 5, and 7, we first determine the least common multiple (LCM) of these numbers. The LCM is (2^1 \times 3^1 \times 5^1 \times 7^1 = 210). For a number to be a perfect square, all prime factors must have even exponents. Thus, we square the LCM, yielding (210^2 = 44100). Therefore, the smallest positive perfect square that is divisible by 2, 3, 5, and 7 is 44100.
What is the least perfect square divisible by 8 9 10 and how?
3600 is the smallest perfect square divisible by 8,9 and 10. Work out the prime factorisations for each of the numbers 8, 9, 10: 8 = 23 9 = 32 10 = 2 x 5 So the perfect square must be a multiple of the lcm of 8, 9 & 10 = 23 x 32 x 5 to be divisible by all three numbers. All perfect squares have even powers for all their primes (in their prime factorisation), so to make all the powers even the smallest multiplier of this is 2 x 5, giving 24 x 32 x 52 = 3600.
What is the least number which is a perfect square and is divisible by each of the numbers 16 20 and 24?
360
What is the smallest positive integer n such that 2n is a perfect square 3n is a perfect cube and 4n is a perfect fourth?
To find the smallest positive integer ( n ) such that ( 2n ) is a perfect square, ( 3n ) is a perfect cube, and ( 4n ) is a perfect fourth, we analyze the conditions for each case using prime factorization. Let ( n = 2^a \cdot 3^b \cdot k ), where ( k ) is coprime to 2 and 3. For ( 2n ) to be a perfect square, ( a+1 ) must be even and ( b ) must be even. For ( 3n ) to be a perfect cube, ( a ) must be divisible by 3 and ( b+1 ) must be divisible by 3. For ( 4n ) to be a perfect fourth, ( a+2 ) must be divisible by 4 and ( b ) must be divisible by 4. By solving these conditions simultaneously, the smallest ( n ) that meets all conditions is ( n = 108 ).
What is the smallest positive integer that has exactly 6 perfect square divisors?
the answer is 144, it is divisible by 1, 4, 9, 16, 36, and 144.
What number is a perfect square and the sum of 2 perfect squares?
25 = 9 + 16 There are many more sets like these. This one has the smallest numbers.
What are the characteristics of a perfect square?
divisible by 2
