Question

The LCM of two numbers is 1320 and their HCF is 6. If the sum of the numbers is 186, then their difference is​

Answer 1

Step-by-step explanation:

Here is your answer,

Given that,

Product of two numbers = 1320

HCF = 6

LCM = ?

Product of two numbers = LCM x HCF

1320 = 6 x LCM

LCM = 1320/6

LCM = 220

Hope it helps you!

Answer 2

Given,

LCM of 2 numbers = 1320,

Their HCF = 6,

Their sum = 186.

To find,

Their difference.

Solution,

Firstly, let the two numbers be x and y.

Now, the relation between the HCF, LCM, and product of two numbers is,

the product of two numbers = HCF × LCM

For the given numbers,

HCF = 6, LCM = 1320. So,

x·y = 6×1320

⇒ xy = 7920     ...(1)

Now, the sum of these two is given as 186.

⇒ x + y = 186     ...(2)

From equation (2),

y = 186 - x     ...(3)

substituting this value of 'y' in equation (1), we get,

x(186 - x) = 7920

⇒ 186x - x² = 7920

⇒ x² - 186x + 7920 = 0

Solving the above quadratic equation, we get,

x = 66, x = 120

For the above values of x, from equation (3), we get,

y = 120 when x = 66, and,

y = 66, when x = 120

So, the two numbers are 120 and 66.

Now, their difference will be,

120 - 66 = 54.

Therefore, for two numbers having LCM = 1320, HCF = 6, and sum = 186, their difference will be 54.