Question

the hcf of two numbers p and q is 5 and their lcm is 200 the product pq is.​

Answer 1

Answer:

The product of two numbers is 1000.

Step-by-step explanation:

Highest Common Factor:

• The Highest common Factor of two or more numbers is the largest number that divides evenly into all the numbers from a group of numbers.
• The Highest common factor is abbreviated as HCF.            

Least common multiple:

• The least common multiple of two or more numbers is the number that can be divisible by both the numbers.

• The least common multiple is abbreviated as L.C.M.

Relation between HCF and LCM:

The relation between HCF and LCM is given by

       Product of two numbers = HCF and LCM of two numbers

Let p and q be two numbers.  

Given HCF of two numbers is 5.  

          LCM of two numbers is 200.  

      By the formula,

   Product of two numbers = HCF of numbers × LCM of numbers

                                       pq = 5×200

                                       pq = 1000

  Hence, the product of two numbers is 1000.

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Answer 2

Answer: The product of two numbers p and q is 1000.

Step-by-step explanation:

Concept:

• Highest Common Factor: The greatest number that totally divides two numbers is known as the Highest Common Factor (HCF). The Greatest Common Divisor (GCD) is another name for the Highest Common Factor (HCF). The HCF of two numbers can be determined in a variety of methods and one of the method is the prime factorization method which is one of the easiest ways to get the HCF of two or more numbers.      

• Least common multiple: The smallest positive number that is a multiple of two or more numbers is call the least common multiple abbreviated as LCM.

• Relation between HCF and LCM: The product of LCM and HCF of the given natural numbers is equivalent to the product of the given numbers.

Step 1: Let p and q be two numbers given in the question.  

Given,

HCF of p and q = 5.  

LCM of p and q = 200.  

Step 2: Now, from the relation above, we can write,

Product of two numbers = HCF of numbers × LCM of numbers

⇒ pq = 5×200

⇒pq = 1000

Final ans: Hence, the product of two numbers is 1000.

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