Three numbers are in the proportion of 3 : 8 : 15 and their LCM is 82…

The ratio of the three numbers is 3 : 8 : 15

Let the numbers be 3x, 8x, and 15x

Here x is their HCF

LCM of 3x, 8x, and 15x = 120x

According to the question,

120x = 8280

⇒ x = \(\frac{8280}{120}\)

⇒ x = 69

So, the HCF of the numbers is 69