Today, Harry mowed the lawn and weeded the garden. Usually, he mows the lawn every 6 days and weeds the garden every 4 days. How many days is it until Harry will again mow the lawn and weed the garden on the same day?
Mows on days 6, 12, 18, 24
Weeds on days 4, 8, 12, 16, 24
12
To find out how many days it will take for Harry to mow the lawn and weed the garden on the same day, we need to find the least common multiple (LCM) of 6 days and 4 days. The LCM is the smallest number that is divisible by both 6 and 4.
To find the LCM, we can list the multiples of each number until we find a common multiple:
Multiples of 6: 6, 12, 18, 24, 30, 36, ...
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, ...
From the lists above, we can see that the smallest number divisible by both 6 and 4 is 12. So, it will take Harry 12 days until he mows the lawn and weeds the garden on the same day again.