Two numbers are in the ratio 5 : 8 and the product of their highest common factor and least common multiple is 6760. What is the sum of these numbers?

Two numbers are in the ratio 5 : 8 and the product of their highest common factor and least common multiple is 6760. What is the sum of these numbers? Correct Answer 169

Given:

Two numbers are in the ratio = 5 : 8

The product of HCF and LCM of the numbers is 6760

Formula used:

The product of HCF and LCM of two numbers is equal to the product of the two numbers

Calculation:

Let the numbers be 5x and 8x

According to the question:

5x.8x = 6760

⇒ x² = 169

⇒ x = 13

Hence the numbers are (5 × 13 = 65) and (8 × 13 = 104)

∴ Sum of the numbers = 65 + 104 = 169