Find the smallest square number which is completely divisible by each of the numbers 10 ,16 and 34
Answers
Step-by-step explanation:
One thing you need to know about perfect squares: if you work out the prime factorization (hereafter, PF) of a perfect square, each of its factors appears an even number of times. For example 3*3*5 = 45. Since the factor 5 only appears once (and one is not even), we know that 45 isn’t a perfect square. But 3*3*5*5 = 225, which is a perfect square. We know it’s a perfect square because each of its factors appears twice, and 2 is even.
One thing you need to know about perfect squares: if you work out the prime factorization (hereafter, PF) of a perfect square, each of its factors appears an even number of times. For example 3*3*5 = 45. Since the factor 5 only appears once (and one is not even), we know that 45 isn’t a perfect square. But 3*3*5*5 = 225, which is a perfect square. We know it’s a perfect square because each of its factors appears twice, and 2 is even.The PF of 10 is 2*5. 10 is not a perfect square, because 2 and 5 only appear once, and one is odd.
One thing you need to know about perfect squares: if you work out the prime factorization (hereafter, PF) of a perfect square, each of its factors appears an even number of times. For example 3*3*5 = 45. Since the factor 5 only appears once (and one is not even), we know that 45 isn’t a perfect square. But 3*3*5*5 = 225, which is a perfect square. We know it’s a perfect square because each of its factors appears twice, and 2 is even.The PF of 10 is 2*5. 10 is not a perfect square, because 2 and 5 only appear once, and one is odd.The PF of 16 is 2*2*2*2. 16 is a perfect square, because 2 appears four times, and four is even.
One thing you need to know about perfect squares: if you work out the prime factorization (hereafter, PF) of a perfect square, each of its factors appears an even number of times. For example 3*3*5 = 45. Since the factor 5 only appears once (and one is not even), we know that 45 isn’t a perfect square. But 3*3*5*5 = 225, which is a perfect square. We know it’s a perfect square because each of its factors appears twice, and 2 is even.The PF of 10 is 2*5. 10 is not a perfect square, because 2 and 5 only appear once, and one is odd.The PF of 16 is 2*2*2*2. 16 is a perfect square, because 2 appears four times, and four is even.The PF of 24 is 2*2*2*3. 24 is not a perfect square, because 2 appears three times, and 3 appears once. Three and one are both odd numbers.
One thing you need to know about perfect squares: if you work out the prime factorization (hereafter, PF) of a perfect square, each of its factors appears an even number of times. For example 3*3*5 = 45. Since the factor 5 only appears once (and one is not even), we know that 45 isn’t a perfect square. But 3*3*5*5 = 225, which is a perfect square. We know it’s a perfect square because each of its factors appears twice, and 2 is even.The PF of 10 is 2*5. 10 is not a perfect square, because 2 and 5 only appear once, and one is odd.The PF of 16 is 2*2*2*2. 16 is a perfect square, because 2 appears four times, and four is even.The PF of 24 is 2*2*2*3. 24 is not a perfect square, because 2 appears three times, and 3 appears once. Three and one are both odd numbers.Any multiple of 10, 16, and 24 must contain each of their prime factors at least as many times as they appear in the numbers being multiplied. So for example, the LCM (least common multiple) of 10, 16, and 25 must contain four factors of 2 (since 2 appears four times in the PF of 16), one factor of 3 (since 3 appears once in the PF of 24, and nowhere else), and one factor of 5 (since 5 appears once in the PF of 10, and nowhere else. Here is the PF for the LCM of 10, 16, and 24
There you have it: 3600 is the smallest square number which is completely divisible by 10, 16, and 24.
Answer:
there is 3600 is smallest square number is completly divisible by 10 16 34