Question

if lcm of two numbers in 180 hcf is 15 and sum of them is 105 what is the difference​

Answer 1

Hey!

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LCM × HCF = a × b __________ (i)

Given,
LCM = 180
HCF = 15


Solving equation (i),

a × b = 180 × 15 = 2700 _________ (ii)

Now,

(a - b)² = a² - 2ab + b²

Rewriting it as -

( a - b )² = (a + b)² - 2ab - 2ab
(a - b)² = (a + b)² - 4ab

Keeping the values,

(a - b)² = 105² - 4 × 2700
(a - b)² = 255
a - b = √255

a - b = 15

Thus, the difference between the given two numbers is 15.

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Hope it helps...!!!

Answer 2

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Refer the attachment.