Question

The hcf and lcm of two numvbers are 12 and 72 respectively. if the sum of thesenumber is 60 then one of the number will be

Answer 1

Given:

Let the two numbers be x & y

x+y = 60..............(1)

H.C.F= 12, L.C.M= 72

H.C.F × L.C.M = PRODUCT OF 2 NUMBERS

12 × 72 = XY

864 = XY

X= 864/y..............(2)

Put this value of x in eq 1

x+y= 60

864/y + y= 60

(864+ y²)/y = 60

864 + y² = 60 y

y² -60y +864=0

y² -36y -24y+864=0

y(y-36)-24(y-36)=0

(y-36)(y-24)= 0

y-36= 0

y=36

y-24=0

y=24

Put the value of y= 36

x+y=60

x+ 36= 60

x= 60 -36= 24

x= 24

If y= 36, then x= 24

If y=24, then x= 36

Hence, the numbers are 36 & 2