Question

lcm of two no is 45 times their hcf.if ome of the no is 125 and sum of their hcf and lcm is 1150 find other no​

Answer 1

GIVEN :-

• Lcm of two numbers is 45 times hcf .

• Sum of their hcf and lcm = 1150

• One number = 125

TO FIND :-

• Other number

SOLUTION :-

  Let ,

   Lcm = x

   Hcf = y

   Other number = z

  According to the first condition ,

     $\sf\longrightarrow y=45x \ \ \ \ \ \ \ \ \ \ \ \ \ \ .................(1)$

   According to the second condition ,

     $\longrightarrow\sf x+y=1150 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...................(2)$

   Put $\sf y=45x$ in Eq (2) ,

    $\longrightarrow\sf x+45x=1150\\\\\longrightarrow 46x = 1150\\\\\longrightarrow\bf x = 25$

 

    Substitute x in Eq (1) ,

     $\longrightarrow\sf y = 45\times25\\\\\longrightarrow \bf y = 1125$

     $\bf Product \ of \ two \ numbers \ = LCM \times HCF$

      $\longrightarrow \sf 125z = 25\times 1125\\\\\longrightarrow 125z = 28125\\\\\longrightarrow \bf z = 225$

• Lcm = 25

• Hcf = 1125

• Other number = 225