A least common multiple word problem about caring for a lawn

Baxter waters the lawn every 3 days and mows it every 7 days. He both watered and mowed the lawn July 2. When will he next water and mow on the same day?

Solution

Let us write down all the dates Baxter will water the lawn in July.

July 2: water the lawn

July 5: water the lawn

July 8: water the lawn

July 11: water the lawn

July 14: water the lawn

July 17: water the lawn

July 21: water the lawn

July 24: water the lawn

July 27: water the lawn

July 30: water the lawn


Now, let us write down all the dates he will mow the lawn

July 2: mow the lawn

July 9: mow the lawn

July 16: mow the lawn

July 24 : mow the lawn

July 31 : mow the lawn


After a close examination, we can see that he will water and mow the lawn on July 24.

The method above though is lengthy and time consuming. Is there is quicker way to get the same answer? Yes!

Just get the LCM of 3 and 7

LCM(3,7) = 21

21 days from July 3 will take us to July 24.