Latest self Aptitude Question SOLUTION: HCF of 2472,1284 and a third number 'n'is 12.If their LCM is 8*9*5*103*107.then the number 'n'is..

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HCF of 2472,1284 and a third number 'n'is 12.If their LCM is 8*9*5*103*107.then the number 'n'is..

sonam tripathy (11 years ago)

Solved Piyush Jain Read Solution (6)

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Read Solution (6) :

Piyush Jain  (11 years ago)

2472=8*3*103
1284=4*3*107
so n = 4*3*x
dividing by hcf
2472/12=2*103
1284/12=107
lcm/12=2*3*5*103*107
x=lcm/first*second
x=2*3*5*103*107/2*103*107=3*5=15
number is = 15*12=180

Is this solution Helpfull? Yes (18) | No (14)  

S R Y Farhan  (8 years ago)

HCF * LCM = Product of numbers (formula used )
n1 =2472
n2=1284
n3=n
HCF = 12
LCM = 8*9*5*103*107
n = (HCF * LCM )( n1*n2)
on solving n = 15 .

Is this solution Helpfull? Yes (12) | No (19)  

vishnu priyaa kannan  (7 years ago)

Farhan and rakesh your formula is right but that formula is applicable only for two polynonials . In question we have three polynomials so this formula is not applicable. so if u take hcf for the first two numbers the numbers will be 206 and 107. When you are taking LCM for that two numbers you get 2^3*3*103*107 the remaining when compared with question is 3*5 so the number taking hcf must be 15 so 15*12=180 so the third number must be 180.

Is this solution Helpfull? Yes (5) | No   

Shubham Raj  (8 years ago)

@rakesh,,,nd s r y farhan
your ans is wrong becz 'n' number is always divisible by 12
so n is 15 impossible

Is this solution Helpfull? Yes (4) | No (4)  

rakesh  (8 years ago)

HCF*LCM=n1*n2*n
n=12*8*9*103*5*107/2472*1284=15

Is this solution Helpfull? Yes (3) | No (10)  

Ashwin Patidar  (7 years ago)

2472 = 2^3×3×103
1284 = 2^2×3×107
HCF = 2^2×3
LCM = 2^3×3^2×5×103×107
HCF of the numbers is the highest number which divides all the numbers.
So N should be a multiple of 2^2×3
LCM is the largest number that is divided by the given numbers.
As LCM contains 3^2×5 these two are from N.

So FINAL ANS
N = 2^2×3^2×5^1

Is this solution Helpfull? Yes (1) | No (4)  

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