[47] Three numbers which are co-prime to each other are such that the product of the first two is 119 and

For Competitive Exams

Three numbers which are co-prime to each other are such that the product of the first two is 119 and that of the last two is 391. What is the sum of the three numbers?

Explanation:

Since the numbers are co-prime, their HCF = 1

Product of first two numbers = 119

Product of last two numbers = 391

The middle number is common in both of these products. Hence, if we take HCF of 119

and 391, we get the common middle number.

HCF of 119 and 391 = 17

=> Middle Number = 17

First Number $=\dfrac{119}{17}=7$

Last Number $=\dfrac{391}{17}=23$

Sum of the three numbers = 7 + 17 + 23 = 47

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