The LCM of two numbers is 126 times their HCF. If their HCF is 7 and the difference between the two numbers is five times the HCF, then the sum of the two numbers is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 161
Let the two numbers be x and y
HCF = 7 → x = 7a, y = 7b (a and b are co-prime)
LCM = 126 × HCF = 126 × 7 = 882
x × y = HCF × LCM = 7 × 882 = 6174
7a × 7b = 49ab = 6174 → ab = 6174 ÷ 49 = 126
Difference = 5 × HCF = 35 → x − y = 7(a − b) = 35 → a − b = 5
a × b = 126, a − b = 5 → a = b + 5
(b + 5) × b = 126 → b² + 5b − 126 = 0
b = 9 → a = 14
x = 7 × 14 = 98
y = 7 × 9 = 63
Sum = 98 + 63 = 161