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.