Question

En mi barrio el camion que recoge los embases de plastico viene cada 3 dias , el que recoge el papel de reciclar cada 8 dias y el que recoge las pilas usadas cada 2 semanas ¿dentro de cuantos dias coinsidiran los tres camiones?

Answer 1

In 168 days or 24 weeks

Explanation:

Now, we have 3 trucks coming on different days but we want to know the

number of days the three will be around together

For the plastic container truck we have 3 days per trip

for the paper container trip, we have 8 days per trip

For the used battery, we have 14 days per trip (14 days is same as two weeks)

Now the key to getting our answer is knowing the lowest common multiple of

3, 8 an 14 days

That would be ;

168

The lowest common multiple of 3,8 and 14 is 168 days

Answer 2

168 days

Explanation:

To find the day that all three trucks will coincide, we need to find the least common multiple of the period of the trucks, that is, 3, 8 and 14 days.

First we need to decompose the numbers into their prime factors:

3 -> 3

8 -> 2 * 2 * 2

14 -> 2 * 7

Then, we need to check the maximum number of times that each factor appears in a number:

2 -> 3 times

3 -> 1 times

7 -> 1 times

Then, we multiply these numbers considering the amount of times they appears:

2 * 2 * 2 * 3 * 7 = 168

So after 168 days the trucks will coincide