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.
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 = 17
So,
HCF = 17
LCM = 30 × 17 = 510
Product = 17 × 510 = 8670
The product of the LCM and HCF is 8670.
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