Question

The product of two digit two numbers is 1944.their LCM is 6 times of their GCD. find the Smaller number is?​

Answer 1

Answer:

The smaller number is 18 .

Step-by-step explanation:

Given as :

The product of two digits number = 1944

The L.C.M = 6 × G.C.D

Let The smaller number = x

And The larger number = y

According to question

∵ The product of two digits number = 1944

So, x × y = 1944

We know that

Product of L.C.M and G.D.C = product of numbers

So, L.C.M × G.D.C = x  × y  

∵ L.C.M = 6 × G.C.D           ........1

So, 6 × G.C.D × G.D.C = x  × y

Or, G.D.C ² × 6 = 1944

Or, G.D.C ² = $\dfrac{1944}{6}$

Or, G.D.C ² = 324

Or, G.D.C = $\sqrt{324}$

Or, G.D.C = 18

So, The value of G.D.C = 18

The number = x = 18 a

And y = 18 b

From eq 1

L.C.M = 6 × G.C.D  

Or, L.C.M = 6 × 18 = 108

So, The value of L.C.M = 108

18 ab = 108

ab = $\dfrac{108}{18}$

ab = 6

The co - prime number for ab = 6 is

( 1 , 6 ) , (2 , 3 )

So, The number are ( 18 , 108) and (36 , 54)

So, The number are 18 , 108

Hence , The smaller number is 18 . Answer