Correct Answer - Option 2 : 150
Given:
HCF of two numbers = 15
LCM of two numbers = 315
Concept:
LCM = HCF × Product of prime factor of two numbers except HCF
Calculation:
Let, the numbers are a and b
a = 15x
b = 15y [Where x and y are prime to each other]
According to the question,
⇒15 × x × y = 315
⇒ xy = 21
Given,
a > 15 and b > 15
15x > 15 ⇒ x > 1
15y > 15 ⇒ y > 1
Now, xy = 21
Factors of 21 are = 1, 3, 7, 21
x and y cannot be (1 , 21) or (21, 1) because x and y should be greater than 1
⇒ (x, y) = (3, 7), (7, 3)
⇒ a = 15 × 3 = 45
b = 15 × 7 = 105
⇒ a and b are 45, and 105 respectively
∴ Required sum = (45 + 105) = 150
