If the Sum of Two numbers is 55 and the HCF and LCM of these Numbers are 5 and 120 respectively, Then the Sum of the Reciprocals of the Numbers is equal to ?

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Find out about two numbers that total 55, share a factor of 5, and have a common multiple of 120. Learn how the sum of their reciprocals is connected in this intriguing math challenge.

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Find out about two numbers that total 55, share a factor of 5, and have a common multiple of 120. Learn how the sum of their reciprocals is connected in this intriguing math challenge.

If the Sum of Two numbers is 55 and the HCF and LCM of these Numbers are 5 and 120 respectively, Then the Sum of the Reciprocals of the Numbers is equal to

The sum of the reciprocals of the number is 11/120.

Explanation

Let’s call the two numbers a and b. We know:

  • a + b = 55 (given)
  • HCF(a, b) = 5 (given)
  • LCM(a, b) = 120 (given)

From the relationship between HCF and LCM, we know:

  • ab = HCF(a, b) * LCM(a, b) = 5 * 120 = 600

Now, we can find the reciprocals of a and b:

To find the sum of the reciprocals, we need to manipulate the expression to get a common denominator:

  • (1/a + 1/b) * (ab) / (ab) = (a + b) / (ab)
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Substituting the known values:

Therefore, the sum of the reciprocals of the two numbers is 11/120.

What is meant by LCM and HCF?

LCM stands for “Least Common Multiple,” and HCF stands for “Highest Common Factor,” also known as GCD (Greatest Common Divisor).

  1. LCM (Least Common Multiple): It is the smallest multiple that is exactly divisible by two or more numbers. For example, the LCM of 4 and 6 is 12 because 12 is the smallest number that is a multiple of both 4 and 6.

  2. HCF/GCD (Highest Common Factor/Greatest Common Divisor): It is the largest positive integer that divides two or more numbers without leaving a remainder. For example, the HCF of 12 and 18 is 6 because 6 is the largest number that divides both 12 and 18 evenly.

These concepts are often used in mathematics, particularly in number theory and algebra, and they are useful in solving problems involving fractions, ratios, and simplifying expressions.

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