If the Sum of two numbers is 55 and the H.C.F. and L.C.M of these numbers are 5 and 120 respectively, then the Sum of the Reciprocals of the numbers is equal to

If the Sum of two numbers is 55 and the H.C.F. and L.C.M of these numbers are 5 and 120 respectively, then the Sum of the Reciprocals of the numbers is equal to

To find the sum of the reciprocals of the two numbers given their sum, HCF, and LCM, follow these steps

Let the two numbers be a and b

a + b = 55

HCF of a and b = 5

LCM of a and b = 120

According to the property of HCF and LCM, we have

HCF x LCM = a x b

Substituting the given values:

5 x 120 = 600

So, a x b = 600

The sum of the reciprocals of a and b is given by

1/a + 1/b = (a+b)/(ab)

Substituting a + b = 55 and a x b = 600

1/a + 1/b = 55/600

= 11/120

Therefore, the sum of the reciprocals of the numbers a and b is 11/120

What is HCF and LCM?

HCF, also known as GCD (Greatest Common Divisor), is the largest number that divides two or more numbers without leaving a remainder. LCM, on the other hand, is the smallest number that is a multiple of two or more numbers.

Finding Common Factors:

HCF/GCD is used to find the largest number that divides two or more numbers evenly. It involves identifying common factors among given numbers and finding the greatest value.

Prime Factorization Method:

To determine HCF/GCD, mathematicians often use prime factorization. By breaking down each number into its prime factors and identifying common factors, they can determine the greatest common divisor efficiently.

Calculating LCM:

LCM is used to find the smallest number that is divisible by two or more numbers. It's essential in problems involving synchronization, such as finding the least common multiple of time intervals or repeating events.

Relationship Between HCF and LCM:

The product of HCF and LCM of two numbers equals the product of the numbers themselves. This relationship is crucial in various mathematical operations and equations involving multiple variables.

Applications in Simplification:

HCF/GCD is crucial in simplifying fractions. By dividing both the numerator and the denominator of a fraction by their HCF/GCD, mathematicians reduce the fraction to its simplest form. Learning about HCF and LCM enhances mathematical reasoning and problem-solving skills. It provides a foundation for understanding number properties, manipulating algebraic expressions, and solving complex equations.

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