Question

The sum of two numbers is 50 and their product is 525. The LCM of the two numbers is: 

Options

• 125

• 105

• 85

• 115

Answer 1

105

Explanation:

Let two numbers be a and b.

a + b = 50 and ab = 525

∴ a − b = `sqrt(("a" + "b")^2 - 4"ab")`

= `sqrt((50)^2 -4 xx 525)`

= `sqrt(2500 - 2100)`

= `sqrt(400)`

= 20 

Now, 

a − b = 20

a + b = 50

2a = 70 ⇒ a = 35 and b = 15

So, H.C.F of 15 and 35 = 5

Now, H.C.F × L.C.M = a × b

5 × L.C.M = 525

∴ L.C.M = `525/5`

= 105