The LCM of the two numbers is 495 and their HCF is 5. If the sum of the numbers is 100 then their difference is

The Least Common Multiple (LCM) of two numbers a and b is the lowest number that is divisible by both a and b exactly.

Answer: The difference of the numbers is 10

The relation between the LCM and HCF of two numbers a and b is given by the formula, LCM (a,b) = (a × b) / HCF (a,b)

Explanation:

LCM of two numbers = 495

HCF of two numbers = 5

Use the formula, LCM (a,b) = (a × b) / HCF (a,b) to find the value of a in terms of b

495 = (a × b) / 5

495 × 5 = a × b

a = 2475/b

The sum of a and b is = 100, therefore a + b = 100

Substitute a = 2475/b in the equation a + b = 100 and solve for b.

2475/b + b = 100

2475 + b² = 100b

b² - 100b + 2475 = 0

(b -55)(b - 45) = 0

b = 55, 45

Now when we insert b = 55 in the equation a + b = 100 then we get a = 45

And when we insert b = 45 in the equation a + b = 100 then we get a = 55

So the two numbers are, 45 and 55

Now, the difference between 55 and 45 is 10

Therefore, their difference is 10.