The sum of two numbers is 60, and their difference is $$\frac{1}{6}$$​ of their sum. Their LCM is:

Correct option is A

Given:

Sum of two numbers = 60

Difference of the numbers =$$\dfrac{1}{6}$$​ of their sum =$$\dfrac{1}{6} \times$$​60 = 10​​

Solution:

Let the numbers be x and y, such that:

x + y = 60

x - y = 10

x $$= \dfrac{60 + 10}{2} = 35, \quad y = \dfrac{60 - 10}{2} = 25$$​

Prime factors:

35 = 5 × 7

25 = 5 × 5

So,

​$$\text{LCM}(35, 25) = 5^2 \times 7 = 175$$​