HCF and LCM of two numbers are 7 and 140 respectively. If the numbers are between 20 and 45, the sum of the numbers is = ?

A. 70

B. 77

C. 63

D. 56

Answer: Option C

Solution(By Examveda Team)

HCF of numbers = 7
Let the numbers are 7x and 7y
LCM = 7xy
7xy = 140 (given)
xy = 20
⇒ Possible co-prime factors of xy
= (1, 20), (4, 5)
⇒ Numbers are between 20 and 45
∴ Required number are = 4 × 7 = 28 and 5 × 7 = 35
⇒ Sum of numbers are = 28 + 35 = 63