Two numbers are in the ratio 3:4. If their H.C.F. is 36, find :
(i) the numbers
(ii) their L.C.M.


[tex

2 thoughts on “Two numbers are in the ratio 3:4. If their H.C.F. is 36, find :<br />(i) the numbers <br />(ii) their L.C.M.<br /><br /><br />[tex”

1. ANSWER:

   Given:

   • Ratio of 2 numbers = 3 : 4
   • HCF = 36

   To Find:

   • the numbers
   • their LCM

   Solution:

   We are given that,

   ⇒ Ratio of 2 numbers = 3 : 4

   So,let the numbers be 3x and 4x respectively.

   We know that, HCF of 2 numbers means the maximum number with which both the numbers can be completely divided.

   Hence,

   ⇒ HCF of the numbers 3x and 4x = x

   But, we are given that,

   ⇒ HCF = 36

   So,

   ⇒ x = 36

   Therefore, the numbers are:

   • 3x = 3×36 = 108
   • 4x = 4×36 = 144

   The numbers are 108 and 144.

   Now, we know that, for 2 numbers a and b,

   ⇒ a × b = HCF × LCM

   Here, a = 108; b = 144; and HCF = 36

   So,

   ⇒ 108 × 144 = 36 × LCM

   ⇒ LCM = (108 × 144)/36

   ⇒ LCM = 108 × 4

   ⇒ LCM = 432

   The LCM of the numbers is 432.

   The numbers are 108 and 144 respectively with LCM 432.

   Formula Used:

   • a × b = HCF × LCM

   Reply

2. Answer:

   Numbers=108,144

   LCM=432

   Step-by-step explanation:

   Let the numbers be 3x and 4x

   HCF=36

   HCF=x

   Numbers= 3*36,4*36

   = 108,144

   LCM= 432

   Reply