The sum of two positive integers is 52 and their LCM is 168

Numbers LCM HCF

The sum of two positive integers is 52 and their LCM is 168. What is the ratio between the numbers?

  1. 2 : 3
  2. 5 : 4
  3. 7 : 6
  4. 7 : 8

Answer

Let h be the HCF of two numbers. Let the two numbers be ha and hb.

Given, sum of numbers is 52

ha + hb = 52

h(a + b) = 52

LCM × HCF = Product of Numbers = ha × hb

168 × h = ha × hb

hab = 168

Calculating, we get

h = 4, a = 7 and b = 6

So the numbers ha and hb are 28 and 24.

The ratio of the numbers is 7:6

The correct option is C.