Question

The Least Common Multiple and Highest
Common Factor of two numbers are 60 and 4
respectively. If their sum is 32, then what will
be the difference of these two numbers?
1. 4
2.8
3. 12
4.
20​

Answer 1

LET THE NUMBERS BE X AND Y

GIVEN ,

XY = 60 × 4 = 240 ( AS PRODUCT OF TWO NO.S = HCF OF THAT NO × LCM OF THAT NO)

XY = 240

X = 240 / Y

GIVEN ,

X + Y = 32

240 / Y + Y = 32

Y² + 32Y + 240 = 0

SOLVING ,

Y = -12 OR 20

AS -12 CANT BE CONSIDERED, Y = 20

=> X = 240 / 20 = 12

THEREFORE , NOW THE DIFFERENCE OF THESE NO.S = 20 - 12 = 8