The sum of two numbers is 1580 and their LCM is 18816. Find the two numbers.

Correct option is C

Given:

The LCM of two numbers = 18816

The sum of two numbers is 1580

Concept Used:

Product of two number = HCF × LCM

Solution:

Let the two number be x and y, then

=> X + Y = 1580 now here x = 1580 - Y

=> 1580 ÷ HCF = P

=> 18816 ÷ HCF = Q

=> 18816 ÷ 1580 × P = Q

=> 1580 = 2² × 3 × 5 × 79

=> 18816 = 2⁷× 3× 7²

Clearly HCF of 1580 and 18816 is 12. As per Formula 

=> X × 1580 - Y = 12  × 18816

After solving above equation, we get

=> X = 12 and  Y = 1568

∴ The two numbers are 12 and 1568.