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The product of 2 number is 1280 and their HCF is square of the smallest composite number. What is the LCM of these numbers?
- a)36
- b)80
- c)8
- d)16
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The product of 2 number is 1280 and their HCF is square of the smalles...
Given that the product of two numbers is 1280 and their highest common factor (HCF) is the square of the smallest composite number, we need to find the least common multiple (LCM) of these numbers.
Let's assume the two numbers to be x and y, and the smallest composite number to be n.
- The product of the two numbers is 1280, so we have the equation:
x * y = 1280
- The HCF of the two numbers is the square of the smallest composite number, which means:
HCF(x, y) = n^2
Now, let's find the value of n:
- The smallest composite number is 4 (as it is the product of 2 and 2, both of which are prime numbers).
- So, the square of the smallest composite number is:
n^2 = 4^2 = 16
Now, we have the equation HCF(x, y) = 16.
To find the LCM of x and y, we can use the formula:
LCM(x, y) = (x * y) / HCF(x, y)
Substituting the given values, we get:
LCM(x, y) = (1280) / 16 = 80
Therefore, the LCM of the two numbers is 80.
Hence, the correct answer is option B) 80.
Let's assume the two numbers to be x and y, and the smallest composite number to be n.
- The product of the two numbers is 1280, so we have the equation:
x * y = 1280
- The HCF of the two numbers is the square of the smallest composite number, which means:
HCF(x, y) = n^2
Now, let's find the value of n:
- The smallest composite number is 4 (as it is the product of 2 and 2, both of which are prime numbers).
- So, the square of the smallest composite number is:
n^2 = 4^2 = 16
Now, we have the equation HCF(x, y) = 16.
To find the LCM of x and y, we can use the formula:
LCM(x, y) = (x * y) / HCF(x, y)
Substituting the given values, we get:
LCM(x, y) = (1280) / 16 = 80
Therefore, the LCM of the two numbers is 80.
Hence, the correct answer is option B) 80.
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Community Answer
The product of 2 number is 1280 and their HCF is square of the smalles...
Given:
Product of 2 numbers = 1280
HCF = Square of the smallest composite number
Formula Used:
Composite Number: Composite numbers are those numbers that have more than two factors.
Product of 2 number = HCF × LCM
HCF = Square of the smallest composite number
4 is the smallest composite number.
⇒ (4)2 = 4 × 4 = 16
Product of 2 number = HCF × LCM
⇒ 1280 = 16 × LCM
⇒ LCM = 1280 ÷ 16
∴ LCM = 80
Product of 2 numbers = 1280
HCF = Square of the smallest composite number
Formula Used:
Composite Number: Composite numbers are those numbers that have more than two factors.
Product of 2 number = HCF × LCM
HCF = Square of the smallest composite number
4 is the smallest composite number.
⇒ (4)2 = 4 × 4 = 16
Product of 2 number = HCF × LCM
⇒ 1280 = 16 × LCM
⇒ LCM = 1280 ÷ 16
∴ LCM = 80
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