Correct Answer - Option 3 : 360
Given:
HCF of two numbers id 15 and each number is greater than 15 and less than 120
Formula used:
Product of numbers = HCF × LCM
Calculation:
Let the numbers be 15x and 15y, where x and y are co-prime
Product of numbers = 15x × 15y
⇒ 225xy = 15 × LCM
⇒ LCM = 225xy/15
⇒ LCM = 15xy
By checking options
Option 1
LCM = 15xy = 90
⇒ xy = 6 = 2 × 3
2 and 3 are co-prime
Numbers are 30 and 45
LCM = 90 is possible
Opton 2
LCM = 15xy = 225
⇒ xy = 15 = 3 × 5
3 and 5 are co-prime
Numbers are 45 and 75
LCM = 225 is possible
Option 3
LCM = 15xy = 360
⇒ xy = 24 = 3 × 8
3 and 8 are co-prime
Numbers are 45 and 120, Numbers should be less than 120.
Hence, LCM = 360 is not possible for the given conditions
Option 4
LCM = 15xy = 150
⇒ xy = 10 = 2 × 5
2 and 5 are co-prime
Numbers are 30 and 75
LCM = 150 is possible
∴ LCM cannot be 360
