Question

jamie volunteers at the pet shelter every 3 days and at the food pantry every 6 days. this month he volunteers at the pet shelter on the 3rd day of the month and the food pantry the 6th day of the month. Jamie says that the first time he will volunteer at both places will be on the 18th day of the month because the LCM of 3 and 6 is 18. Does Jamies reasoning make sense? use an example or a counterexample to explain your anaylasis

Answer 1

Jamie's reasoning is incorrect. The first time he will volunteer at both places is on the 6th day of the month, as 6 is the first common multiple in both his volunteering cycles.

Step-by-step explanation:

Jamie's reasoning regarding the first time he will volunteer at both places is actually incorrect. Although 18 is the least common multiple (LCM) of 3 and 6, this is not the correct way to determine the day when Jamie will volunteer at both locations for the first time. The correct approach is to look for multiples of each number and find the smallest common multiple. In this case, because Jamie volunteers every 3 days, he would be volunteering on the 3rd, 6th, 9th, 12th, 15th, etc., days of the month. For the 6-day cycle at the food pantry, he would volunteer on the 6th, 12th, 18th, etc. Hence, the first day Jamie volunteers at both places in the same day would be the 6th day of the month since it is the first common multiple within the sequence of days he volunteers at both places.

Answer 2

Answer: No. Jamies reasoning doesn't make any sense.

Counter example :- Isha decides to go on walk on every 4th day and go for gym on every 2nd day in a month.

Then Isha will do both the things on same day = LCM (4,2)

Now, LCM of 4 and 2 = 4

Therefore, Isha will do both the things on 4th day of the month .

Step-by-step explanation:

Jamies reasoning doesn't make any sense.

Because the LCM of 3 and 6 = 6 not 18[since 6=3×2]

LCM is the least common multiple number of two or more numbers.