Sher Khan, the tiger, goes hunting every 3rd day. Bagheera, the panther, goes hunting every 5th day. If both of them start on the same day, on which days will they be hunting together?
Given: Sher Khan hunts every 3rd day. Bagheera hunts every 5th day. Both start on the same day.
Solution: Sher Khan hunts on multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30... Bagheera hunts on multiples of 5: 5, 10, 15, 20, 25, 30, 35... Common multiples of 3 and 5: 15, 30, 45, 60, 75... LCM of 3 and 5 = 15
Answer: They will hunt together on days 15, 30, 45, 60, 75, ... ∴ They hunt together every 15th day.
Explanation
This is a common multiples problem. Sher Khan hunts on days that are multiples of 3 (3, 6, 9, 12, 15, 18...). Bagheera hunts on days that are multiples of 5 (5, 10, 15, 20, 25...). They hunt together on days that are common multiples of 3 and 5, which are 15, 30, 45, 60...
Solution Steps
Sher Khan hunts on multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30...
Bagheera hunts on multiples of 5: 5, 10, 15, 20, 25, 30, 35...
Common multiples of 3 and 5: 15, 30, 45, 60, 75...
LCM of 3 and 5 = 15
They will hunt together on days 15, 30, 45, 60, 75... (every 15th day)