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