Question

the L.C.M of two numbers is six- times their H.C.F. If the difference between L.C.M and H.C.F is 60 and one of the two numbers is 36 ; find the other number.

Answer 1

LCM =x
HCF = y
Given x = 6y
x-y =60
6y -y =60
5y = 60
y = 12
x = 12*6 = 72
we know that
product of two numbers = HCF× LCM

36 × second no. = 12×72
second no. = 12×72 /36 = 24 Answer

Answer 2

Hi friend, Harish here.

Here is you answer:


Given that,

1) Difference of the HCF & LCM is 60.

2) One of the two numbers is 36.

3)LCM is 6 times HCF.

To find,

The Another number.

Solution,

Let, HCF Be ' x ' , Then LCM is  ' 6×HCF' = 6x.

We know that,

$LCM - HCF =60$

⇒ $6x - x = 5x =60$

⇒ $x = \frac{60}{5} =12$

So, HCF = 12 & LCM =(6 × HCF) = 6 × 12 

We know that,

HCF × LCM = Product of two number.

Let the unknown number be  ' y ' 

Then,

$12 \times 6 \times 12 = 36 \times y$

$y = \frac{12\times 12\times 6}{36}= 24$
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Hope my answer is helpful to you.