If the sum of two co-prime numbers is 11 and their LCM is 30. Find the lower number among the two.

Question of The Day21-11-2022

Answer

Correct Answer : a ) 5

Explanation :

It is given that,

two numbers are co-prime, which means their HCF is 1 since they don't have any common factor apart from 1.

LCM of the numbers = 30

Let the numbers be x and y

Sum of the numbers = x + y = 11

We know that,

For two numbers

HCF x LCM = product of numbers

1 x 30 = xy

xy = 30 .........(1)

x + y = 11 ...............(2)

Substitute y = 30/x from eq. 1 in eq. 2

x + 30/x = 11

x² + 30 = 11x

x² - 11x + 30 = 0

x² - 6x - 5x + 30 = 0

x(x - 6) - 5(x - 6) = 0

(x - 5)(x - 6) = 0

x = 5, x = 6

If x = 5, y = 6

If x = 6, y = 5

Therefore, the lower among x and y is 5.

Hence, (a) is the correct answer.

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