If the product of HCF and LCM of two natural
numbers is 378000, then which of the following can
be their HCF?(1) 66
(2) 130
(3) 34
(4) 20
Answers
Answered by
2
LCM * HCF = 37800
We know LCM is a multiple of HCF.
So LCM * HCF
= HCF * HCF * x = 378000 , x = an integer.
HCF² * x = 10² * 2² * 3² * 5 * 3 * 7
HCF = 20 or 30 or 60 possible.
Answer is (4) 20.
We know LCM is a multiple of HCF.
So LCM * HCF
= HCF * HCF * x = 378000 , x = an integer.
HCF² * x = 10² * 2² * 3² * 5 * 3 * 7
HCF = 20 or 30 or 60 possible.
Answer is (4) 20.
Answered by
1
We know that ,
HCF x LCM = Product of 2 numbers
But HCF is one of the multiples of LCM i.e LCM = HCF x some integer (let's say r)
So, HCF x (HCF x r) = 378000
HCF^2 x r = 378000
378000 can be written as 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 x 5 x 7
Taking squares ,
2^2 x 3^2 x 10^2 x 3 x 5 x 7
So, HCF = 20,30,60
Seeing the options ,20 is the required answer.
Hope This Helps You!
HCF x LCM = Product of 2 numbers
But HCF is one of the multiples of LCM i.e LCM = HCF x some integer (let's say r)
So, HCF x (HCF x r) = 378000
HCF^2 x r = 378000
378000 can be written as 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 x 5 x 7
Taking squares ,
2^2 x 3^2 x 10^2 x 3 x 5 x 7
So, HCF = 20,30,60
Seeing the options ,20 is the required answer.
Hope This Helps You!
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