The HCF and LCM of two numbers are in the ratio of 1 : 30 and the difference between the HCF and LCM is 493. Find the product of LCM and HCF.

Correct option is B

Given:

Ratio of HCF : LCM = 1 : 30

Difference between LCM and HCF = 493

Solution:
Let HCF = x, then LCM = 30x
Given:

30x - x = 493

29x = 493

x $$= \frac{493}{29}$$​= 17

So,

HCF = 17

LCM = 30 × 17 = 510

Product = 17 × 510 = 8670

The product of the LCM and HCF is 8670.