a neighborhood trash pickup comes every 7 days while the recycling pickup is every 12 days after how many days will both the trash and recycling be picked up on the same day
To find the number of days when both the trash and recycling will be picked up on the same day, we need to find the least common multiple (LCM) of 7 and 12.
List the multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, ...
List the multiples of 12: 12, 24, 36, 48, 60, 72, ...
The first common multiple is 28 (which is a multiple of both 7 and 12), so they will be picked up on the same day after 28 days.
Therefore, both the trash and recycling will be picked up on the same day after 28 days.
To determine the number of days it will take for both the trash and recycling pickups to occur on the same day, we need to find the least common multiple (LCM) of 7 days and 12 days.
Step 1: Write down the multiples of 7 and 12.
Multiples of 7: 7, 14, 21, 28, 35, 42, ...
Multiples of 12: 12, 24, 36, 48, ...
Step 2: Look for the smallest common multiple in both lists.
The smallest common multiple is 84, which means that both the trash pickup and the recycling pickup will occur on the same day after 84 days.
Therefore, both the trash and recycling will be picked up on the same day after 84 days.