Ericka and Destiny are roommates, and they have a dog. If neither of them is home, they hire someone to watch the dog. Ericka must go on business trips every 4 months, while Destiny has to go business trips every 6 months. If they both just got back from business trips, how many months will it be before they need to hire someone to look after the dog again? I said the answer would be : 2 months is this right
To find out how many months it will be before they need to hire someone to look after the dog again, we can determine the least common multiple (LCM) of Ericka's business trip frequency (4 months) and Destiny's business trip frequency (6 months).
To do this, we need to list the multiples of 4 and 6 until we find the smallest common multiple:
Multiples of 4: 4, 8, 12, 16, 20, 24, 28,...
Multiples of 6: 6, 12, 18, 24, 30, 36, ...
From the lists above, we can see that 12 is the smallest number that appears in both lists. Therefore, the LCM of 4 and 6 is 12.
This means that after both Ericka and Destiny have just returned from their business trips, it will take 12 months before they both have to leave for a business trip simultaneously again.
Therefore, your answer of 2 months is not correct. The correct answer is 12 months.