Latest CAT Aptitude Question SOLUTION: the lcm of two numbers rs 14 times the their HCF.the sum of lcm and hcf rs 600.if one number rs 80,then the other number is.

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the lcm of two numbers rs 14 times the their HCF.the sum of lcm and hcf rs 600.if one number rs 80,then the other number is.

Asked In CAT MohanRaj (11 years ago)

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shylaja  (11 years ago)

let a and b be any two numbers then,
a*b= [hcf of (a,b)]*[lcm of (a,b)]
given
lcm of a,b= 14(hcf of a,b)
lcm of a,b + hcf of a,b = 600
14(hcf of a,b)+hcf of a,b=600
15(hcf of a,b)=600
hcf of a,b=40


then a*b=lcm * hcf
since a=80,
80* b = 14(hcf)*hcf
80*b=14 (hcf)^2
we got hcf=40
b=14*40*40 / 80
b= 280
HENCE THE ANOTHER NUMBER IS Rs. 280

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sc mandota  (11 years ago)

let hcf=x
then lcm= 14x
hcf+lcm=600
x+14x=600
x=40=hcf
lcm=560
as we know
lcm*lcf=num1*num2
40*560=80*num2
num2=280

so second no. is 280

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