Question

The HCF and LCM of two numbers are 12 and 72 .if the sum of these numbers 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 & 24
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Hope this will help you....

Answer 2

Given :

HCF=12

LCM=72

Let the numbers be X and Y

Sum of two numbers =X + Y =60

HCF x LCM= product of two numbers

12 x 72 = XY------------(1)

864=XY

X=864/Y

Now substitute the value of X in equation 1 we get value of Y.

⇒864/Y + Y = 60

⇒864 + Y² =60Y

⇒Y² - 60Y - 864=0

Now let us find the factors of Y.

Y² - 36Y - 24Y + 864=0

⇒Y(Y-36) - 24 (Y-36)=0

⇒(Y-36) (Y-24)=0

⇒Y=36 , 24

Now substitute the value of Y in equation X=864/Y

we get X value :
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If Y=36 , X =864/36 =24

If Y=24, X =864/24=36

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∴ The two numbers are 36 and 24