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Which of the following statements is correct?
- a)Every prime number is odd.
- b)Every even number is composite.
- c)The sum of two odd numbers is always odd,
- d)The HCF of two given numbers is always a factor of their LCM
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Which of the following statements is correct?a)Every prime number is o...
The correct statement is option 'D'.
Explanation:
HCF and LCM are important concepts in number theory. HCF stands for Highest Common Factor and LCM stands for Lowest Common Multiple. The HCF of two given numbers is the largest number that divides both the numbers evenly. The LCM of two given numbers is the smallest number that is a multiple of both the numbers.
The relationship between HCF and LCM is that the HCF of two given numbers is always a factor of their LCM. This can be explained as follows:
Let's take two numbers a and b. We can write them as a = p1 * q1 and b = p2 * q2, where p1, p2, q1, q2 are prime factors of a and b.
The LCM of a and b is given by LCM(a, b) = max(p1, p2) * q1 * q2.
The HCF of a and b is given by HCF(a, b) = min(p1, p2).
Now, let's find the factors of LCM(a, b). The factors of LCM(a, b) are max(p1, p2), q1 and q2.
We can see that the HCF of a and b, which is min(p1, p2), is a factor of LCM(a, b), which is max(p1, p2) * q1 * q2.
Therefore, the HCF of two given numbers is always a factor of their LCM.
Explanation:
HCF and LCM are important concepts in number theory. HCF stands for Highest Common Factor and LCM stands for Lowest Common Multiple. The HCF of two given numbers is the largest number that divides both the numbers evenly. The LCM of two given numbers is the smallest number that is a multiple of both the numbers.
The relationship between HCF and LCM is that the HCF of two given numbers is always a factor of their LCM. This can be explained as follows:
Let's take two numbers a and b. We can write them as a = p1 * q1 and b = p2 * q2, where p1, p2, q1, q2 are prime factors of a and b.
The LCM of a and b is given by LCM(a, b) = max(p1, p2) * q1 * q2.
The HCF of a and b is given by HCF(a, b) = min(p1, p2).
Now, let's find the factors of LCM(a, b). The factors of LCM(a, b) are max(p1, p2), q1 and q2.
We can see that the HCF of a and b, which is min(p1, p2), is a factor of LCM(a, b), which is max(p1, p2) * q1 * q2.
Therefore, the HCF of two given numbers is always a factor of their LCM.
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Which of the following statements is correct?a)Every prime number is o...
Option D
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